First of all: omegas can top and alphas can bottom. Alphas can bottom for omegas too. Generally during heats omegas prefer to be penetrated and alphas to penetrate but they can just use toys. Alpha ≠ top. Omega ≠ bottom.
With that outta the way here we go.
In most concepts of omegaverse you “present” as your secondary sex during puberty, however some writers may decide to make secondary sex something people are aware of from birth/ very young. Usually the second one ties heavily in soulmate or destined mate* concepts, but the former can as well. You’ll find a lot of stories that show finding out you’re an alpha or omega (or beta) through a national blood/pheromone test at a certain age, or multiple times during life as test results can change slightly over time, in these stories being an alpha or omega doesnt do much until you fully “present” during puberty.
Depending on the level of education in an individual story yes there can be garbage sex ed that tells you almost nothing of what to expect and how to deal with it. These concepts usually relate to omegas that don’t bother to read their “test” results abt their gender and believe they’re an alpha until they suddenly go into heat, or their test results were inaccurate all along. They also relate to stories that portray omegas as “lower class” or simply sex objects. Bad sex ed stories usually include challenging stereotypes as a main focus.
Usually in omegaverse omegas are undesirable to hire due to heats being more frequent than alpha ruts, and thus more disruptive. so they lie about being an omega to get hired, and then either pump themselves full of heat suppressing medication, or call in sick every time. In stories where omegas are treated fairly they just call in normally lol. They keep track of their heats and they work with their job to get time off periodically for it, unless triggered by an alpha’s rut or pheromones, heats are pretty consistent unless they have some sort of condition that makes them irregular. Prostitution is a very common theme in omegaverse due to omega’s not being able to get hired at “normal” jobs and societal pressures.
I imagine workplaces will require a doctors note or something to prove irregular heats etc if someone was abusing the “call out for heat” option. But omegas will often call out a day or so before their heat just to prepare better.
Some betas do pretend to be alphas or omegas to get further in life or to fuck more people. Its seen as sleazy and manipulative.
Alpha/alpha relationships depend on how the author wants to write the concepts of their society or biological instincts. Usually alpha relationships include a lot of domination and sexual fighting with the winner of the fight being the one to top (if they dont already have a dynamic that suits them) switching is common with both alpha and omega same sex relationships. In omegaverse these dynamics are either seen as normal or are extremely frowned upon. Usually they are kept secret to avoid conflict.
Sometimes if an alpha gets extremely aroused they can pop a knot without being inside something, this is common during puberty the same way boners are in teens. Its usually super uncomfortable and sensitive and legit physically cannot go away for at least ten minutes.
Heat cycles do sync. So do rut cycles. Heat and ruts can sync too. Not all omegaverse omegas nest but yeah they do have gc with friends lol.
Yes alphas make it a Job to help with heats. They’re called “heat aids.” In some omegaverse friends help each other through heats too, be it by just being around or sexually. Its usually seen as like kind of embarrassing to hire a heat aid cus it means you have no one else close to you or a bf/gf to stay with you to get you thru it. But its considered “normal” to hire one.
I havent seen a forced to take suppressants as a kink story but some stories have omegas fantasising about being confined to houses or rooms and used only to make babies (they call them “pups” pretty often).
All in all omegaverse is an EXTREMELY varied story device and no one has clear ideas for it, but yeah basically everything op said is a thing.
* A destined mate is someone so compatible with you or your pheromones that you’re considered “soulmates.” Some concepts have this being a supernatural thing, while most keep it to being a pheromone/biological thing.