Bengals are typically smarter than the average cat. They get into things BECAUSE of that. I didn't have to train mine to do anything really. My son did teach him to climb the ladder to his loft bed in five minutes and he climbed up and down every day for the five years we had the bed. He can open doors and has ever been known to jump up and turn on a light(don't know if he meant to do that, but he's done it twice

) He walks on a leash. Best of all, he is the softest, sweetest cat I have ever had, and he is a big snuggle bunny at night.
Bengals are active, so they either need an owner who is home a lot, playing with them, or another Bengal or high energy cat to keep them exercised. Otherwise they will get into everything. Oh, and the running into the door may be because he is bored or trying to get out. My bengal constantly climbs the door jambs of all my doors and sometimes he will run and slide into walls when he can't stop fast enough, LOL. We got two kittens 18 months ago, and he loves having someone to play with.
Marsha
They need a lot of exercise