1 The plumber said he'd stop by
anytime between 10 and 12pm./somewhere between 10...
I'd prefer "sometime" to "anytime". It would be more appropriate to use "anytime" in order to give someone permission to come at whatever (any) time they choose.2 The two bad things bad thing about this apartment is its lighting. Its It is/It's not bright at all, and that its it is/it's on the 5th floor. (Is being on the 5th floor supposed to have some sort of negative impact on the lighting?)
3 There are more cards that you need to avoid than cards that make you win. (is this ok, how would you say this?) OK in context. Sounds informal.
4 We all know how great her taste is /what great taste she has. OK
5 Every time you use a bit of hot water, the water heater tank heats up water fills to maximum capacity again so you have a full tank of hot water.
She is so nice (that) I don't care if she is possessive. OK, strikes me as informal