Don't use F logic it's a pain in the arse, use anything else LS, HCT or whatever meets your speed requirements.
1. Is the CLR of a SN74AHC174 Hex D-Type F-F tied to Vcc if unused? (I think so, want to make sure.)
The F Fast Logic is not so easy to work with especially if you are prototyping on vero, the inputs need to be driven correctly, if you are not careful and have any noise you can destroy them through high current consumption, they can be power hungy, i would advise you to avoid them there are better technologies that are less power hungry, if you must use the F series then read the data sheet very carefully and run them in spec by driving the inputs correctly.