A few questions about Sims 4

First things first, if you're not using mods and you're seeing odd behaviors like these, take them to EA answers headquarters. You want add in the search what you're seeing... like "YA still going to high school" and if there are topics with that up... go into it and check the "me too" and add in what you see to the topic... or if there is no topic start one.This site covers only the use of the modding program sims 4 studio.

To answer the other questions.

1. Young Adults can go to university if you have that installed. If you don't want them to do that, then have them quit university. If they're going to high school and you are not modded, then that is a bug. They should quit on the birthday of Young Adult. Things you can do to move them forward is age them up with a cake or via CAS commands in full edit mode. You maybe able to find a console command cheat that will have them graduate university, you'd have to look that up.... something like "Sims 4 commands to graduate university" should pull up the appropriate commands or MC Command Center mod maybe able to help cheat them out of university promotions or what have you. You could also assign them a job temporarily, maybe that would fix it. It would likely give you the option to "quit" the high school or university "job" to allow you to do another job. then you could quit that one.

2. I know you've said young adults here, but I feel like you're talking about teens. This game has too broad of a scope for age brackets. There's no between stages... like the 1-3 years of teen numbers (17-19) you can be and not be in high school. Teens can't woohoo, ask for marriage or sleep in the same bed. Young adults, however, should be able to do all of those things. If you're not modded then do the first thing I mentioned because it's likely some kind of bug. Teens I believe can "fool around" and "promise to be engaged"... but cannot do anything outside of those things until they're young adults. It's possible that promised or engaged sims maybe broken functionally and you will have to do the first thing I mentioned. Cursory google search did say something about promised teens unable to propose. So you maybe seeing a bug. You maybe able to remedy with a console command or a mod to change the relationships status. MC Command Center is practically required to bypass some of the crazy bugs that are out there these days.

If you want the odd relationship functionality where teens can woohoo and be married (Either teen to teen or Teen to YA) you will need a mod, like MC Command Center or Wicked Whims or the less lewd version Wonderful Whims but you'd have to mess around with the settings and those all can be found on their respective webpages and by default those mods will not allow a teen and a young adult to do anything so you will need to tweak them or just simply make both sims the same age bracket. They have to be YA or older to do anything else. Even if they met in school, had a relationship and one aged up before the other they would still have to both be YA before you could do anything else. Once the YA status comes in, they can't do anything with teens.

3. Adults who are unmarried but in a relationship should be able to sleep in the same bed if they're living together. I'm not sure that they would automatically sleep in the same bed if they weren't living together. They may route to an unused bed or couch in that scenario. If they're living together, they should be able to... but you may need to assign the beds and sides of the double bed. Many of the sims will route to random beds unless they're assigned. You do that by right clicking on the bed with the sim you want to sleep in it and find the assign on the menu. With double beds you can choose right or left.

If you're not modded, do the first thing I mentioned above. If you are modded, first back up these folders (TRAY, SAVE, and MODS) copy them somewhere safe. Then... you will take all the mods out. Then delete anything in the sims folder that has the words "Cache" on it and let the game update. For good measure, you can then try a repair the game at this point. (Do not do that if you've got your mods still in there. It will break your mods. Updates will break your mods... pretty much anything EA does will break your mods. So back them babies up before you do any troubleshooting.) Go in WITHOUT mods and see if you still see the problems. If not, then one of your mods is causing the problem. If it's still there without mods, then do that very first thing I mentioned.

To sus out your mods folder, start by 50/50. Meaning take half out, check the problem, if it exists... take out half until you you don't have the problem. Whenever you lose the problem. you've found the mod.

Example, you have 100 mods. Take out the first 50 and the problem goes away... then you know that the problem is somewhere within the first 50 mods. So take out the second half and put the first half back in. Take out 25 of part one... rinse repeat until you have narrowed down the problem mod. Check for updates to it... if there are none remove that broken mod until someone fixes it.