Can B/C/F/ be used with movement actions like Hypersonic and Charge????

It can be used with charge for sure since that allows for a close combat attack and BCF can be used during a close combat attack. I'm sure it works the same way with HSS, however I cant think of someone that has that power combo. That would be very nasty indeed. A great charge/BCF combo character is the V Kobra Fanatic for only 24 points. The 8 attack value is the only real downfall.

BCF will work with Charge, but not HSS. HSS grants a free action that can be used to make a ranged or close combat attack. BCF is activated by a close combat action.