Re: #3, perhaps so. I have seen many a good CI process go to hell over time. I could argue no one would have a CI process if in the beginning it wasn't making life easier. It would seem no CI process survives contact with the dev team.
Re: Modules, generally I do as well, but what is a "module"? A function? A class? A library? A plugin? An extension? A listener? A handler? A subscriber? A publisher? A DAO? A DTO? An in-memory service? A networked service? A microservice?
The philosophy that I subscribe to is continuous integration is not the same as "everyone check into the same branch anytime they want as often as they want" but also that it is not "everyone work in their own branch until time has run out and we have to force all of our stuff to work together." That middle ground can be very tough to find, but I find that if the CI system and the architecture are not designed to work together, devs will always thrash around between those two extremes.
If you throw a frog in boiling water it will freak out. But if you throw a frog in cold water and slowly bring it to a boil, it will never notice.
I actually like to submit completed modules when they are ready. I find constant pushing makes things a lot more complicated.
edit: fix terrible spelling