Can one keep chewing down on premolars and molars and eventually make them crooked and pushed into the gums more?

Chew down: It is unlikely that normal chewing forces will move teeth "down." if you have a dysfunctional bite, it is possible to cause some misalignment of the teeth. The only way to properly move teeth is with orthodontics.

Not really: Your teeth would wear away or break before you ere able to move them apically into the bone. Yes, a bite that is off can cause teeth to shift. Teeth also shift naturally with age, so an occlusion that was perfect years ago might be off just a bit now, especially if you've had some dental treatment or lost teeth. See your dentist for an evaluation.

Tipping, yes: If you have lost other teeth around them, then they can tip into the space where the other teeth were. You can have abrasion (like toothbrush), erosion (like acids), or attrition (like grinding), but intrusion (the teeth being pushed into the bone is not likely.