What's the best xp/hour method to soloing dungeons?

Most likely mediums, given that you can complete them in about 10-15 minutes.

 

While in a solo c6 small, there aren't enough monsters to supply food drops and it possible that that will cause a time delay making it take like 10 minutes as opposed to 3-5, leading to less exp per hour.

Do I only kill monsters in rooms that are necessary? Rooms I'll probably run through a lot, stuff like that.

well, to get the fastest xp, in teams, people only clear rooms for guardian doors or for puzzles where you need an interface open that gets interrupted by combat, like making things from stone blocks for the statues.

 

I'm not sure if it'd be any different for solos.

Would c1 rushing the first few and doing mediums the last 5 be good?

I'd probably do more than 5 meds, but whatever works for you.

Would c1 rushing the first few and doing mediums the last 5 be good?

 

Might be a good idea to do more than 5 meds at the end though. But you should do as you feel like. If that is how you want to train it and you feel that you get decent xp, then go for it.