Yes, you still exercise. You PT five mornings a week in most units. It's just that you only go for an hour or hour and a half a day, instead of several hours like in Basic Training.
No, that'll be fine. Just don't write anything sappy on the outside, our Drill Sergeants considered anything on the outside fair game. One girlfriend kept writing stuffy like "Lovey Baby I Miss You" all over her pink envelopes. That guy was teased.