In reverse order:
You cum quickly because your prostate is being stimulated. Which is more or less the whole point of bottoming, innit? Speaking only for myself, when a guy cums fast because my dick is inside him, literally my only reaction is GO ME I AM THE KING OF SEX. Like, seriously, it's a huuuuuuuuuuuuuuge ego boost. If the guys you're getting with are making you feel bad about it, stop fucking them because you deserve better.
Beyond that, the usual 'lasting longer' advice applies: have a preemptive wank shortly before you get together with someone; depending on your refractory period, why not cum twice in a single session--once by mouth or hand, again when you get fucked; when you're by yourself, include anal stimulation in your wanking and edge yourself, basically train yourself to resist the urge.
For your other issue...I have never knowingly experienced that specific sequence of events happening with a bottom, but my ex (cis male) would relatively frequently get me all the way inside him, then very suddenly need me to pull out, and then would be absolutely ready to get fucked for a long time. Maybe this is just how your body reacts?
I think a lot of queer men have unrealistic expectations around sex. Buttsex is tough! The anal sphincters evolved to push stuff out, not take it in. Small wonder that you're not reacting like a pornstar! I say accept that this is just how your body works, and any man who doesn't respect that is a man who doesn't deserve sex from you.