> 2) I want to disable wrapping and I see that there is an
> `isearch-wrap-function` but it is a variable not a custom and it is not
> documented in detail what is expected to be there.

isearch-wrap-function could be customizable in the same way with 3 options:
pause before wrapping (default), no pause, no warp at all.

> 3) In general many of the customizable variables in isearch are defined
> with defvar so it is difficult to distinguish between internal and user
> exposed ones. Just to mention some examples:
> isearch-push-state-function, isearch-filter-predicate, the hooks,

And these as well.

> Are there any WIP related?

There is no WIP until you create a feature request.