I need to show a form, which is a choice form for other form, but it does not linked to any catalog and just gets the data from internet. I want to use standard choice handling, but could not imagine how to define everything needed for this form to work.
And could you explain a little how the selection mode works because there is nothing in the books.

I understand that there is a ChoiceProcessing procedure
Syntax:
ChoiceProcessing(<SelectedValue>, <ChoiceSource>)

and
NotifyChoice
Syntax:

NotifyChoice(<SelectionValue>)

but what should I define any special parameters for the form, run it in special mode o something else?

In your case you need to create a common form and add a custom Select command which closes the form using

Close(YourSelectedValue);

Object.YourAttribute = OpenFormModal("CommonForm.YourFormName");