The three-batter minimum and the cap on number of pitchers go together. If there's a three-batter minimum, it becomes a lot harder to actually use eight (or more) relief pitchers in any rational, consistent way.
As for injuries - pitchers can be removed before facing three batters if they get hurt... but if they come out of a game due to injury prior to facing three batters, they're required to go on some kind of DL, and become unavailable to the club for some period of time. Seven days? Ten days? Don't have the specific answer here, but it wouldn't be difficult to prevent "fake injury" abuse.
I'm not endorsing these changes, but I can see how they could work.
The one I really don't like is "draft advantages to winning teams and penalties for losing teams." If a club wins 100 games, they get "draft advantages"? How is a struggling club supposed to get better, if they suffer draft penalties when they're already short of talent? I could see this strategy if there were eight MLB clubs, all in very large cities, all with the ability to support $200 million payrolls - and wide-open free agency, which allowed all clubs to compete equally for talent. But how do the Pirates, or the A's, or the Twins, or etc., etc., etc., compete with the Yankees, Red Sox, Phillies, Dodgers, etc., in such a regime? Unless you simultaneously take ALL club revenue from ALL media sources, put it into a single pool, and divide it equally among clubs (which is NOT going to happen), this would drive smaller franchises right out of the league.