How can I treat corns?

You can try. Filing with an emory board then protecting with a silicone toe sleeve. Podiatrists can offer more permenant solutions.
Depends. If not causing pain, you don't have to. If you choose to, there are over the counter corn removers that use acid, there are pumice stones too. If necessary, your physician can shave it/pare it down. Wear shoes that fit w/o rubbing. If you are diabetic seek advice from your physician prior to self treatment.

Related Questions

How can I treat and prevent corns?

Prevent them. By wearing properly fitting shoes, treat them by filing with an emory board.
Corns. Corns/calluses form from friction against the skin, but also moisture is needed. On top of changing shoes and socks, try moisture control by using spray deodorant on your feet. This helps decrease moisture. Also file them down daily in the shower or use Vicks vapor rub to soften them up. Lastly, off-load the areas to take pressure off and prevent reformation. Hope this helps! Good lucks!