Game shape has an effect on performance, but it is pretty easy to keep most of your players in good game shape, so its effect may not be that significant, unless you just bought a player who had been playing and was in atrocious game shape.
Nobody really knows how the MVP is determined, but I'd think more minutes played would end up looking better. Lack of stamina (and lack of skills) hurt.
Game shape can drop from overplaying, but it probably has to be in the 100+ range. In the high 80s and 90s it might be more about a 50-50 chance of a drop or gain.
I'm not sure what you mean by minimal players. If you mean that a team has 7 or 8 players, they are putting themselves at a lot of risk for injuries or foul problems, but they might be saving some salary. They probably aren't training as many players as they could.
18 players is really too many. But I think BB gives new teams that many so that they can feel that owners can feel that they are actively developing their team, even it simply means discarding the weak players. It probably helps to understand the game better if they can use some weak players in a game and see how poor their performances are.