Depends. Most important is if your implant surgery is recent. Make sure you speak with your doctor about this. In general, if you had recent surgery, how you deal with your immediate post operative positioning with your bra could be very important. If you are beyond 6 months after surgery, it should not matter. http://drkulick.com/procedures_ba.php.
Not likely. Although there are concerns with wearing supportive bras at night even without implants. Over the long term if this will affect your tendency for sagging or ptosis.
Probably not. Assuming you have not undergone breast augmentation recently, it is unlikely that the use you (or not) of garments, including bras, will “hurt” your implants in any way.