Is it okay to work out all days of a week?

Yes.: Exercise everyday is great. However, your body does need time to recover. I.E. If you do upper body weights one day, do something different (like running or swimming) the next. Don't do any strenuous activity for a week straight. That's a setup for injury and you won't get the beneficial results you would expect. Keep it varied and work different muscle groups on a staggered schedule.

Yes: All in moderation and good balance between cardiovascular and weight training. Daily exercise is actually the current recommendation. Any daily exercise program at your age should be started gradually and preferably with a help of a professional.