How Injuries are Handled

If a player on your roster gets injured and is forced to miss time, is there a "DL" spot you can place him on, and are you able to pick up a replacement without dropping a player? And how does that work with the salary cap? Does the injured player still count towards the cap?

Nope. No DL

You have to plan accordingly. If you draft injury-prone players, make sure you draft decent backups. Or you can draft low-risk players (their injury ratings are in green instead of black) and not worry too much about backups.

If you play DH leagues the AI will not let you drop below 9 players (8 for noDH) though some may end up out of position (the worst fielding possible)--so if you carry 13 hitters only 4 will be injured max simultaneously---AI will ignore injuries until more than 9 hitters are eligible.