Mm if you allow me to answer, in order 1 till 5...
Q1 :
Q2 : yes. Yep, like some kind of untold rule of nature.
Q3: Nope. Omega can be impregnated by both alphas or betas. But for a beta to impregnated an omega is in low rate of chance. The percentage is low. Because the amount of sperm. Alphas have lots more amount of sperm than betas. And i read so in forum, it said their sperm is more active than any betas.
Q4: I am not sure how to answer this one. So i will have not to answer to avoid mistakes here.
Q5: Nope. As long as the partner have a womb, and in good condition, they can be imprgnated. In short, betas can be paired with women alphas (only), women betas (only), and omegas (both men and women). But, the chance to impregnated male omegas is lower more than women omegas, i can said almost 0 chance, but not impossible.
This is one of the best explanations of the Omegaverse genre I've ever seen. Hope it helps ! http://www.mangago.zone/read-manga/junjou_shounen/uu/junjou_shounen-chapter-1/9/
Actually it depends on the story and the kind of omegaverse there is. Taking other omegaverse into account, a beta can be paired with a male alpha too. And I think that would make a lot of sense since the sperm rate of an Alpha is strong enough to pretty much instantly impregnate an Omega, and(even if it takes a longer time, more "tries" than the Omega one) a male alpha can pretty much reproduce with a beta, be it female or male
Btw to answer the two questions that were left would be
Q1: Technically, no. Originally in the entire omegaverse universe the "destined pair" rule only goes for alphas and omegas. Though it shouldn't be misunderstood as thinking that betas can't be in a reproductive relationship with either of them. When it comes to biting, the only effective "marking" can only be done by an alpha since their job in that society is to dominate and Mark the pair they choose.
To answer your 4th question, I believe its another form of racism that belongs to that universe. Not everyone can think about omegas being similar to the other gender types since they don't care enough about it. But of course not everyone is like that. There are alphas who respect omegas, and vise versa.

Can someone please explain(excluding what we've seen in this yaoi):
- Can Betas not bite a Omega, they same way an Alpha can, like with all the same circumstances e.g. the omega not being able to have sex with anyone else?
- Are Omega made to be with an Alpha? Like some kind of untold rule of nature.
- And can Omegas only fully breed with Alphas?
- And if yes, why are they treated lower than Beta, if their existence is kinda really necessary for an Alpha?
- And do Beta HAVE to be with other Beta's? Can't they aim for an Alpha?