Am I allowed to play something besides an ADC if I queue as bot and get the role?

Look you can, but there's a few things to consider:

1. Does it work with your team? If you've got a Graves/Quinn top/jungle, or a corki mid, or something like that, then maybe it could work. If you don't have a marksman anywhere else, realize that your team doesn't have anyone to help take down turrets effectively. It's a key part of the game.
2. Is your team okay with it? Playing off meta goes over a lot better when playing with a premade. If you're with random solo queue players, especially in ranked, they don't want you to have fun experimenting. They want you to play your best and have the best shot at winning.
3. Can you handle being flamed? People will get mad at you if you don't win pretty hard
4. Are you okay with losing? The meta exists for a reason - largely, it works. You may find success with something off meta (and it may even become meta if it's not just a fluke that made it successful), but by and large you'll lose more than you win with these kind of strategies.

Depends if your team would be fine with it, though usually hardly ever the case.

Though only if people are as accepting as me, because I let literally anyone work with me, even if extremely off-meta.

You should be fine playing Malzahar (or anybody) bottom lane. Playing non-meta champions has never been punishable.

Quite frankly, so long as you don't steal somebody else's role (i.e. taking Malzahar Mid or Top after queuing for Bot), you should be fine.

That said, I would expect that your teammates may not react in the most positive (i.e. non-toxic) manner to such a pick.

I would recommend playing malzahar adc only with friends, but if you don't feed intentionally nor flame no one can really tell you what to play. Obviously if you get a bad score expect others to report you hard for trolling.

You can technically play anything you want...now whether or not it'll be effective and whether or not your team mates will cooperate is another thing entirely.

You can play Malzahar bot if you want. There's no rule against it. Expect people to bitch you out for it though, especially if you do poorly.

The reason it's called "Bot" instead of "ADC" is Riot hoping people can make AP champions (or fighters) work in that role. Just mention it to your team before hand.

I wouldnt because it would be less effective than a normal ADC. that being said, you most definitely can - I would just let your teammates know verbally in chat as well