CB GroupJive doesn't have that functionality so no it's not doable without implementing it yourself. It however can be implemented using CB Auto Actions. The below should work.

Global
Triggers: gj_onAfterCreateGroup
Type: Email
User: Automatic
Access: Everybody
Action
To: query
To Query: Subject: EMAIL_SUBJECT_HERE
Body: EMAIL_MESSAGE_HERE

That should email every user when a group is created. I would recommend caution with this. It'd be easy to spam users with too many emails by doing this and could result in your email domain being blacklisted if too many people report you as spam.

The below would mimic what the internal behavior is doing.

Global
Triggers: onAfterUserRegistration
Type: CB Activity
User: Automatic
Access: Everybody
Action
Mode: Activity
Method: Create
Stream: Profile Activity
Asset: profile.[user_id].registration
Load By: None

That asset would just result in the same title displayed as the internal activity, which is "joined the site". Note that is a language string so you could just override it for example. To avoid that you could create your own asset. Below for example would work fine.

Asset: profile.[user_id].registered
Title: My Title
Message: My Message

Sure, that would rely on a Joomla content event. You can find more information about Joomla content events below.

manual.joomla.org/docs/next/building-extensions/plugins/plugin-events/content/

Specifically you'll be using onContentAfterSave and to use a Joomla event in CB Auto Actions you'll need to prefix it with joomla_ giving joomla_onContentAfterSave. Since these are filtered by context you'll need an article context with is com_content.article. Below is the details for the onContentAfterSave event and what variables it contains.

manual.joomla.org/docs/next/building-extensions/plugins/plugin-events/content/#oncontentaftersave

This can all be put together using the below example.

Global
Triggers: joomla_onContentAfterSave
Type: Email
User: Automatic
Access: Everybody
Conditions
Condition 1
Field: Custom > Value
Custom Value: [var1]
Operator: Equal To
Value: com_content.article
Condition 2
Field: Custom > Value
Custom Value: [var3]
Operator: Equal To
Value: 1
Condition 3
Field: Custom > Value
Custom Value: [var2_catid]
Operator: Equal To
Value: CATEGORY_ID_HERE

Replace CATEGORY_ID_HERE with the id of the category you want this applying to. You can use an "In" condition to supply a comma list of category ids as well if you need more than 1 category. It should only apply to newly created articles due to the var3 ($isNew) check. Next just configure the rest of the email however you like.

Ok, latest CB Gallery build release now has the slashed eye indicator for published state implemented. I've implemented it throughout all views that have indicator icons including grid views for both albums and media. Even media modal windows will indicate unpublished next to the menu dropdown.

I am not (yet) familiar with autoaction plugin, so i will be happy if you can provide such example, thank you !

This might be quite complicated if you've no CB Auto Actions experience, but the configuration example is as follows for the auto action. Basically what we'll be doing is overriding the date handling for the CB Activity logging behavior for CB Gallery activity. Some of the below might be confusing if you've no CB Auto Actions experience so I'd recommend just installing it and exploring it first before putting together auto actions. This assumes you still want to go through with doing this. I don't particularly recommend it since it causes media to go outside the flow of things, but it's up to you.

Global
Triggers: activity_onBeforeActivityEntitySave
Type: Code
User: Automatic
Access: Everybody
Conditions
Field: Custom > Value
Custom Value: [cb:parse function="getAsset" class="var1" /]
Format Functions: Yes
Operator: Is REGEXP
REGEXP: /^gallery\./
Action
Method: PHP
Code: Parameters
Reference Variables: Variable 1

I've confirmed the above works to force the activity date to be the current datetime causing it to ignore the date of the gallery entry itself.

By sending an email I meant use an Email action. That's what I used in my tests with success. Are you sure your gateway id is correct? You need to provide the number under the Id column and not under the # column.

It's possible to act on payment state change as well. That maybe more ideal since you're just needing to act on successful payments from paypal. Below is tested working as well.

Global
Triggers: onCPayAfterPaymentStatusChange
User: Automatic
Access: Everybody
Conditions
Condition 1
Field: Custom > Value
Custom Value: [var4]
Operator: Equal To
Value: Completed
Condition 2
Field: Custom > Value
Custom Value: [var2_gateway_account]
Operator: Equal To
Value: YOUR_PAYPAL_GATEWAY_ID_HERE

This is just acting on a payment basket being marked completed for a specific payment gateway. Below was used in both test examples.

Global
Type: Email
Action
Subject: Payment Test Email
Body: Success!

Ok, took a bit longer but have a much cleaner solution. Format Functions in CB Auto Actions now support inline Query and Code execution (must be a Super User to toggle on and use these!). This allows substantially easier inserting of the invoice HTML wherever you like in whatever auto action you like. The below for example will example the invoice HTML. Note you'll need to update to latest CB Auto Actions build release before you can utilize this.

Global
Triggers: onCPayAfterPaymentStatusChange
Type: Email
User: Automatic
Access: Everybody
Conditions
Field: Custom > Value
Custom Value: [var4]
Operator: Equal To
Value: Completed
Action
Subject: Invoice
Body: Parameters
Format Functions: Yes
Format Code Function: Yes

The complicate comes from determining if the basket contains merchandise payments or not. This would apply to all baskets basically. So to find if a merchandise was purchased it'll require an additional condition that checks what is in the basket. The below should work for that.

Field: Code
Custom Code: Operator: Equal To
Value: 1

This should allow the condition to match if the basket contains at least 1 row item that's a merchandise.

Your conditions are probably is what is failing. The database state is considered in transit. It can change based off webhooks, what state they're moving into/from, etc..

Are you needing to act on the payment status change or the subscription status change? onCPayAfterPaymentStatusChange is the correct trigger for payment status changes and onCPayUserStateChange is the correct trigger for subscription status changes. With both you should be using the variables already provided to them instead of querying for information. After selecting either trigger you should see what variables are available to them just below the Triggers parameter.

Since you mentioned payment being finalized and subscription being active I'd act on subscription state change with onCPayUserStateChange. The below for example should work fine.

Global
Triggers: onCPayUserStateChange
User: Automatic
Access: Everybody
Conditions
Condition 1
Field: Custom > Value
Custom Value: [var2]
Operator: Equal To
Value: A
Condition 2
Field: Custom > Code
Code: Operator: Equal To
Value: YOUR_PAYPAL_GATEWAY_ID_HERE

This will work on renewals as well. If you only want it on first payment you'll need to add a condition against the $reason. Example as follows.

Field: Custom > Value
Custom Value: [var6]
Operator: Not Equal To
Value: R

That should be doable since the option selection is stored with the basket, the subscription, and POST data so it's possible to pull that value from either in CB Auto Actions. The main issue will be how you've defaults setup. You'd need to have admin approval enabled by default in CB > Configuration > Registration so that you're turning it off rather than on.

As for what trigger to act on. Probably best to do this the same way CBSubs does. Directly before registration is completed. So the onCPayBeforeUserRegistration trigger should work here. It has limited information in it as follows.

Basically only have the array of plans selected in addition to the user being registered. So this is doable, but it will take PHP experience as you'll be overriding the registration behavior of CBSubs. For example the below will force the registration approved, but needs additional checks like checking the option selection from POST data.

Global
Triggers: onCPayBeforeUserRegistration
Type: Code
User: Automatic
Access: Everybody
Action
Method: PHP
Code: Output
Display: return

The only way to conditionally display content like that is with substitutions. You won't be able to do this from CB Content Module because it has no user to act on since they're not logged in.

The best I can suggest is to just replace the confirmation page entirely and redirect them away to language specific pages. That is doable with CB Auto Actions. The below should work.

Global
Triggers: onAfterUserConfirmation
Type: Redirect
User: Automatic
Access: Everybody
Conditions
Condition 1
Field: Custom > Value
Custom Value: [confirmed]
Operator: Equal To
Value: 1
Condition 2
Field: Custom > Value
Custom Value: [cb_country]
Operator: Equal To
Value: DE
Condition 3
Field: Custom > Value
Custom Value: [cb_gender]
Operator: Equal To
Value: female
Action
URL: YOUR_ARTICLE_URL_HERE

Replace YOUR_ARTICLE_URL_HERE with your language specific article so you can display whatever language specific content you want. I don't know how you're handling age so I didn't add that condition so you'll need to add that yourself.

I suppose another option is to auto login after confirmation. CB Auto Actions includes a system action for this already, but it requires their account to be fully confirmed and approved before it'll auto login. Then you could display whatever you like since they'll be logged in.