I'll just tackle the base-running one.
The principle is that over the course of a season, good/fast base-running is going to result in more runs than bad/slow base-running. Mookie Betts is going to produce more runs with his feet than J. D. Martinez, for example. That's easy enough to understand. The WAR calculations attempt to determine exactly how many runs a good base-runner has added, compared to a baseline player-the infamous "replacement player". The replacement player is sort of the same thing we hear called an AAAA player.