If the login emails are the same they will get banned on both version of the game. I'd not recommend doing that if one account is precious to you and the other isn't so you bot the shit account lol
Yes, as they are linked together both accounts will be banned. I would not recommend botting on any account you care about, bot rates are decently high currently.
They are linked but they don't share bot reports. Like if you get banned on OSRS for botting, the RS3 team won't look into your account much further as opposed to OSRS keeping your account on watch for repeat offenses.