what feature/functionality are you looking for exactly?

1)Option to difference the ones that are ready to "Date" or not, maybe with a heart icon on ther profile. (I created a Field in the Field Managment and put Date? and customer would have to type "Yes" or "no" thats a really quick solution but with no features.

Create a checkbox fieldtype with the name as "Read to date?". This would show on profile as "Read to date?: Yes". You could also set it on a tab that is in a not shown on profile tab position then use a delimiter field with the below substitution to show an image instead.

[cb:if cb_rdytodate="1"]<img src="[cb:config param="live_site" /]/images/rdytodate.png" alt="Yes" />[/cb:if]
[cb:if cb_rdytodate!="1"]<img src="[cb:config param="live_site" /]/images/notrdytodate.png" alt="No" />[/cb:if]

Please note the above is just an example, but gives you understanding of how it needs to be structured.

2)Filter and listed the ones that wants to date and disscard the ones that didnt choose that option when register for the first time.

With the above done you'd add a basic filter for the checkbox field checking if the value is 1.

3)Common search options when searching like "Male" or "Female" and ages 18 to 24 / 25 to 30 / 30 to 40 / 40 and on... Looking for Men / Woman / Ready for.. hang out / relationship, etc..

All can be done creating basic fields such as a date field or a select field. Then add them to your userlist for them to be searchable.

4)Other features (not neccesary) wink, kick, blow kiss, not interested, interested, lets connect...

CB has no such features, but it's possible a plugin is available to provide them. I recommend checking Joomla.org

I recommend reviewing the documentation found in Advanced downloads section for help setting up basic fields and userlists.

1. A new 'image' type field containing the image name ("member-icon.gif") with the image in /images/comprofiler/. This just gave me a Pending Avatar icon. It seems like it is being moderated even though only the main avatar is supposed to be moderated?

Image moderation applies to all images, not just avatar.

2a. A new 'text' type field containing a link to the image ("<img src="/images/graphics/member-icon.gif">". This just gave me the link as text.

2b. Wrapping the link in Sourcerer ("{source}{/source}") tags just gave me the Pending Avatar icon again.

Just use a delimiter field and supply the HTML directly. If you need user data in it or IF statements you can use substitutions to accomplish those. For more on substitutions please see tutorials within my signature.