You seem to be doing fine so far. I highly recommend real cardiac rehab, not just going to the gym. This is a 12-week (beginning 6 weeks post-op), carefully monitored, graduated aerobic exercise program for which most insurance will pay. I was an active guy with an athletic background, but I found this program to be of great help. They went a bit too slow at first but eventually it became challenging and my exercise tolerance increased immensely and steadily. You will find nearly all the other rehab clients are MUCH older and have had coronary artery disease and are given much more restricted exercise regimens. So, you may feel quite out of place, but unless you are VERY conscientious and consistent with exercise on your own, the cardiac rehab program is the best thing you can do post-op to get back into good or even better shape. After that, you should have no restrictions on exercise at all, unless there is some other reason for that. As you said, the mechanical valve and warfarin should not affect your lifestyle (unless perhaps you were a big-time drinker, in which case the valve and warfarin would encourage a positive change in lifestyle). I'm almost 2 years out. After the first 4-5 months, with the rehab under my belt, there has been essentially nothing that reminds me I have a bionic valve.
BTW, I started sleeping on my side almost immediately in the hospital, with a few pillow supports. If you follow the sternal precautions in the way you move around, there's no reason not to if it is comfortable. I kept a pillow propped under my top leg and in front of my thorax and under my top arm when sleeping on my side for the first couple of weeks. I've never liked sleeping on my back and was glad I didn't have to.