Usually male betas and alphas can not get pregnant. But female alphas can 'make' children. A lesbian family would be possible, but have never seen an author who has taken care of this matter.
I think that children are usually tested early, so that they already know before their first heat, if they are an omega and they usually stay home during heat and also take pills if they do not have a partner. In most omegaverses, alphas and omegas can form a bond (by bite) that will make them no longer attractive to others.
I've never seen it said that "male betas and alphas can't get pregnant" anywhere though. The bite thing is true and i have seen manga where betas are desctibed as "normal humans", though that seems more at the author's discretion. From my experience, it is usually the case that alphas can get pregnant as well, there is a lot of mentioning of alphaXalpha to "protect the genes", it doesn't ever mention alpha males working differently in these situations besides maybe less likelihood of getting pregnant than the other sexes. The mark/bond is an important detail as well.
I only heard that male omegas has a womb.
It of cause depents on the writer, but for me even omegaverse has it's rules.
Theres a good page with a lot details here:
http://fanndists.tumblr.com/post/115147143334
The pregnancy part says: "Omegas, beta females, and occasionally alpha females can become pregnant."
And for alpha+alpha I guess one of them is female.
"Male" and "female" aren't the only two sexes now, the reality is that the 3 new sexes (O/A/B) are the primary sexes at this point with "male" and "female" being used as descriptors for outward appearance. This is because now everyone can get pregnant as everyone has a functioning penis/testicles AND womb, the probabilities of pregnancy just differ for the sexes and increase/decrease depending on their partner. No, their bodies don't make them "intersex", that is a birth defect, an abnormality. The 3 new sexes are a natural state like a male having a penis and testicles irl. The alphas and omegas are made for each other at a genetic level, the pheromones attract them to each other as, at their core, their sole purpose is to reproduce. Omegas project their pheromones out against their will, alphas can control their pheromones until in the presence of an omega. No, this does not mean they can't be raped, both alpha and omega alike, however there is a difference between rape and rough pheromone sex, namely the intentions. In an omegaverse, with the above taken into account, sex can only be labelled rape if the intentions were rape. Otherwise all the accidents would be rape as well. Society in omegaverse knows how this all works, that is why in a lot (really most) of omegaverse omegas are hated, a young alpha with a promising future can be innocently minding his business while walking down the street, suddenly a random omega goes into heat and any alphas in the immediate area are literally forced to find, impregnate and mark the omega even if the have a lover and don't want to. The pheromones ruin relationships, they cause parents to worry that their children are going to accidentally get someone pregnant/get pregnant at a young age, etc.