should I carry a medium spinning reel as well as my baitcaster with me? or does the baitcaster cover everything?

It's a good idea to have both at your beck and call.

My opinion carry both. I do....I can't cast a 2"-3" grub on baitcasting gear to be quite honest.

Personal choice, I don't even own a freshwater b/c reel, nothing I fish for can't be handled on a 2000 series spinner.

if you have the space, why not.

I definitely recommend having both tools. You have to be pretty good at baitcasting to skip lures under overhanging brush or under docks without backlashing. Also, when the wind is blowing the baitcaster is my tool of choice because the lighter spinning rig gives me "horseshoes" of line to deal with. The baitcaster is my tool of choice, but, I don't hesitate to pick up my spinning gear when I need it.