- If I modify the values in the Kunena, these are not reported in the CB profile.

Of course, Kunena doesn't pass information to CB.

- if I modify the values in CB, these are reported in the Kunena profile.

Right, that's how it's supposed to work.

The problem is that in Kunena there is a button to modify the profile, but in the Kunena form, not in CB. Only when I saved the form, Kunena skips in the CB user profile.

Then you don't have Kunena configured properly to integrate with CB. Ensure CBs Kunena plugin is enabled from Kunena Forum > Kunena Plugins. Kunenas profile should be disabled when you've CB integration configured properly.

The Kunena's profile was disabled until last K. update.
In Kunena CB Integration all the option are "Yes" and in Kunena integration the option "Enable Kunena Profiles" is "No".

Within Kunena Forum > Kunena Plugins > Kunena - Community Builder Integration all options should be "Yes". It's working fine in all my tests with Kunena 2.0.1.

In my opinion is duty of CB to read and to write these in the other main extensions, not of these to pass info to CB.

We don't expect anyones extension to pass information to CB. This is why we have plugins to pass information to those extensions. CB Forums does, Forum Integration does, CB Articles pulls the articles to CB. If all else fails CB Auto Actions can be used with a Query action or if API is needed a PHP action to pass information to 3rd party extensions.

At the moment we have a user profile of Joomla (with the new fields) not synchronized with CB, a user profile of K2 not synchronized to CB, a user profile of Kunena not synchronized, and so for many other extensions.

Joomla, K2, and Kunena profiles are not to be used. Once CB integration is turned on it will use CB API to render CB information. We've communicated with K2 and Kunena to ensure this happens. If you need further information passed to Kunena such as date of birth then configure it in either CB Forums or Forum Integration.

We have already all the post in the Kunena profile and all the articles in the K2 profiles.
To have all the information in a central point like CB is a good thing, but if it is not necessary always to work around the problems related the integration and to wait that Kunena, K2, XYZ make some modify to their extensions.

No one has to make modifications. The integrate to CB is already there. We have direct communication to K2 and Kunena teams. I've confirmed both integrations are there and that both are working fine.

Also because often the functionality of these are more "functional" of those of CB.
For example, now that I have seen the Kunena's profile i can say that this is better, more clean and more aesthetically appealing.

We don't pull profile data from 3rd party extensions. Nor will CB ever do so. I suppose you could write a plugin to do this if you like, but we've no plans to do so.

Too me, but I see the Kunena profile.

You shouldn't see the Kunena profile and if you are you need to post to Kunena as perhaps there is a bug or perhaps there is configuration they would be more aware of then I, we're not Kunenas developers.

1) people has need the fields of the standard extension, like Kunena and K2. If you publish a plugin for these, why you are not planning the related fields or a some function to create them if not already present in DB?

Then don't enable the CB integration for K2 and Kunena as they're optional and you don't have to use them.

2) Now, some extensions need also the "User - profile" fields (of Joomla 2.5, not fields of some other strange extensions ). So, these must be present in DB, too.

Then use CB Auto Actions to pass their CB profile data to Joomlas profile database table after registration and profile update. The alternative is to contact those other extension developers and ask them to integrate CB. They're welcome to contact us directly for API help as we've done with K2 and Kunena.

3) It is not enough to create the fields in CB ( in manual mode): for example in CB Forum you ask for gender field the values 1 or 2, but in K2 the gender is M and F and obviously a previous gender field can have a different values, like "Male"/"Female"). At least, there are some instructions to replicate the values correctly?

CB Forums handles the translation of values to Kunenas appropriate values. You can use 1/2, Male/Female, or _UE_MALE/_UE_FEMALE for your CB field value and it'll properly pass 1 (male) or 2 (female) to Kunena.

We don't pass anything to K2 so can't help you there; you'd need to ensure proper translation of value before sending it to K2 in your integration. Once K2 CB integration is used you can't even reach K2s profile so this shouldn't be an issue.

4) It is not enough to synchronize the fields; for example the new user in CB are not created in K2 and I'm searching for instructions to do this.

You don't need to create a user in K2 with CB integration enabled in K2 as K2 profiles won't be used. Otherwise if you still want to create a user in K2 you can do so with a Query action in CB Auto Actions with the after registration trigger. If API is needed/wanted you could use a PHP action to load and execute K2 API to create the user (probably best approach, contact K2 for API usage information).