I'm nearsighted in one eye and farsigted in the other eye, will I need two different contacts?

Monovision. Depends on visual needs and current visual acuity uncorrected, plus presence of presbyopia. See an optometrist.
Depends. This may be an advantage as you age as with the proper contacts or sometimes without correction at all, you can see things for the full range. I always recommend that you see an ophthalmologist for these questions. Optometrists are not as fully trained and you would like the complete picture I am sure.