Should be able to use the phone as a hotspot and run apps at the same time, only limiting factor is the 4G/3G bandwidth available. I've used mine as a hotspot for 3 Ipad minis at once and used Facebook etc at the same time with no issues (well other than the phone getting very warm and the battery draining like a sink....).
Not sure re the time difference but webcam times shown often seem behind real time, may be some buffering going on?