1. how to make exactly same form with Toolset, I should to open new topic, right?
Given the length of the ticket here it'd be the best yes.
I understand the Form Field you have now is just adding a Post Meta (Post field) with the ID or Name of the Post chosen, to the current edited/created post, is it?
This should be doable in Forms, by using for example post reference field, or just a field that you update programmatically when submitting the form.
If you need detailed help with this we can start a new ticket.
It works however the same way as with your current setup.
You make a form, add a generic Field (for example) and populate that field with a ShortCode which returns all the posts you want.
Later you save that generic fields value to a post meta using the cred_save_data hook for it.
https://toolset.com/documentation/programmer-reference/cred-api/#cred_save_data
https://toolset.com/documentation/user-guides/inserting-generic-fields-into-forms/
If you wait a little, there will not even be custom code needed for this, instead you'll be able to populate those generic fields with Views.
This is estimated to be released within the coming releases, so it can be expected soon.
While your form is fast and easy, it does not setup a post relationship at all, which is what you steadily outlined as your goal in other tickets.
Updating a Custom field of a post with whatever other data that you get programmatically (just as with that form) is easy as well in Toolset Forms.
2. 1) Form what not create the entries (posts) > Formidable have in settings simple checkbox for that (so simple and easy).
I do not know what you mean. Forms that create no posts? Can you explain?
2. 2) Form with repeatable field groups in initial part of form (Toolset hardly can do it as there is no parent post for that).
Those are repeating fields of a post, it's not the same as a repeatable field group, I think.
If you study the difference of a repeating field and a repeatable field group in Toolset you will notice that repeating fields as well can be added within the same form as you use to create the post.
Repeatable Field Groups are technically Posts. Those need new forms.
3. So, to conclude, now I have 101% fully functional Formidable Form what working as I want. However, I would like to not use external tools and to have it with Toolset Forms.
I think so, all you do there is populate a Select Field with some data you get by php and that is definitely possible in Toolset Forms.
New ticket only because this one is too long, not because its out of topic.
Thanks!