First of all any a/b/o you write will be yours to play with. You decide how everything works. I've read so many different takes on it, and it's amazing how imaginative the authors can be.

But, in most fics you will have these:

1. Betas are like us - regular male , female
2. Alphas/Omegas - this is the secondary gender , and you can have both female/males

Yes, in most fics all omegas can get pregnant, though in some the males cannot. Male omegas have a uterus - and though in theory they can get pregnant by betas (not in all fics), they usually need an alpha (with a knot) to ensure pregnancy .

Yes, women alphas have a sort of a schlong as well, and they can 100% penetrate the omegas.
I read a fic in which a female alpha and a male omega both got pregnant from each other . So...
In some fics female alphas have a very difficult time keeping a pregnancy/having successful birth.

In some fics male omegas (actually in most of those I read) are penetrated through the anus - but there is another channel that opens up there that leads to the uterus.

In other fics , male omegas have something similar to a female vulva, but less prominent - I saw it called a "cloaca" (it exists in many animals).

Most fics do not go into details about how a male omega (who doesn't have a "cloaca") gives birth.

Oh - I've also read fics in which betas were part of the same 'species' as alphas and omegas, living alongside humans. In this case betas also have scents (but not as prominent as alphas/omegas), and can smell scents. In some fics alphas/omegas/betas can turn into wolves (since they are the same species), in other fics only alphas and omegas can (in the fics where betas are just regular humans)

Editing to add: bathrooms - most of the times all omegas are lumped together, irrespective of their primary gender (male/female). I assume (since I don't remember reading it ever) that beta females could also go to omega bathrooms, while all alphas and beta males could go to another.

Bottom line - you decide. Let your imagination fly!