Joomla 2.5 to Joomla 3.2 is not a migration. You do not need to use a migration extension in this case. If you've a backup of your site or your 2.5 site is still in tack then go back to it and perform a normal upgrade to 3.2 using the below steps.

1. Navigate to Components > Joomla! Upgrade
2. Click Options
3. Set "Update server" to "Short Term Support"
4. Click "Save & Close"
5. Refresh
6. Click upgrade button to upgrade to Joomla 3.2

Please keep in mind any extensions, plugins, etc.. installed that are not compatible with Joomla 3.2 could cause issues. It's recommended to basically disable all non-core extensions and re-install them over top of themselves once you upgrade to ensure they're Joomla 3.2 compatible.

Please note anytime a migration is done only jUpgrade and SP Upgrade are recommended by Joomla. No other migration extensions have been approved.

Aside from the above there's nothing more I can advise in regards to migrations or upgrade of core Joomla. Proper upgrade shouldn't cause any issues for CB or its plugins.

One strange thing happening with CB/Cbusbs is that if we show plan at registration, CB is not able to send the confirmation email (although correctly specified in cbsubs plan to do that using CB default). If we do not show plans at registration the confirmation works but of course we cannot automatically assign our free plan to the newly registered user.

By default the confirmation will send after payment is completed. So this could be awhile if you're using Offline gateways for example. You may want to set confirmation to send before payment.

Also when a new user register (with plans showing at registration) he got a: "The subscription is restricted to logged in users" that never happened.

Check the Access tab of your plans and ensure both Usergroup and View Access Level are at minimum set to "Public".

And regarding the Email confirmation. I have set to use "CB Default configuration".

The default behavior is to send after payment. You may want to try it with send before payment.

If I decide to leave the registration as a normal CB registration and only use Merchandise plans for my users (which are in fact the only used plans) would it bring any possible issue?

All plans except free are basically treated the same in this regard.

I mean that I had this Free Subscription plan that is indeed Free and Lifetime. I created that months ago to create a CBsubs record for every user. But in the reality this plan is not giving anything to users because when they buy our services they use merchandise plans.

Free lifetime plans shouldn't cause any such issues. A free lifetime plan should become active immediately and not affect the flow of registration. Is it the only plan for you that's causing problems with confirmation? Ensure CBSubs is set to create subscriptions for free lifetime plans within CBSubs > Settings > Global.