Conservation of mass only works in a perfectly closed system, meaning absolutely no outside interference. This leaves only the universe as a whole or some theoretical perfect vacuum as possibilities. Conservation of mass and energy breaks down when studied anyway, they just use it as a baseline because it works outside of theoretical physics. For your purposes, however, I'd say that the conservation of mass is probably the least of the issues you face when turning a man into a frog, but I'll go along --> If you're to turn a man into a frog, you're right in that the whole of the person could not go into it, so the rest of him would have to do -something else-.
When we renew ourselves, the cells do not come back a little worse, the individual cells are the exact same. Your cells replace themselves by division, and can divide only a given number of times, after which they stop. New cells are constantly being made, while old cells are constantly being destroyed. As one gets older, however, the rate at which new cells are made decreases as more and more cells stop dividing. Thus, you have 'less' 'healthy cells;, as opposed to 'less healthy' 'cells'. : P
If we completely stopped renewing ourselves we would wear out extremely quickly. If you somehow managed to avoid any kind of injury, which would cause you to bleed out, or sickness, where you would run out of T cells faster than an aids victim, your skin wouldn't last very long and you'd die of chafing.