I started playing Dungeon Defenders recently having a lot of fun with it, still trying to figure out what stats affect what. Does increasing my hero cast rate increase how fast I can summon/repair towers during the combat phase?
Yes, it increases your summoning and repairing speed in combat, but you get an extra modifier when in build phase.
From the Dungeon defender wiki about hero casting rate:
Like most other stats it has diminishing return, graph from the Stat Progression Graph wiki page:
While leveling it could be a good idea to place some points in hero casting speed, but once you get a good godly set or better gear you should get plenty of points in hero casting speed from items so you can place your points in other stats.