Well here goes. I am still an undergrad so I can't promise I am 100% correct but as to your first question; push ups are mainly an endurance activity and will mainly recruit slow twitch (type I) muscle fiber. Whereas squats and dead lifts will recruit fast twitch muscle fibers (type IIb). Push ups will not only use your creatine phosphate metabolic pathway but it will also tap into your glycolytic and oxidative pathways. The squats and dead lifts tax mainly your phosphocreatine. This explains why push-ups may be performed for a longer duration than squats. (Phosphocreatine last a max of 15 sec & glycolysis last up to 2 minutes). Going back to muscle fibers a quick explanation is slow twitch is good for marathon while fast twitch is good for sprinting. Every person has both but genetics determine the % of each. I hope that's clear. Please ask if I left anything out.
As for number 2 this is actually a good idea to do those activities before your compounds because they help recruit fibers and increase blood flow to the muscle. Just don't go to fatigue with them. I would say at most half to max. So if you can do 20 push-ups only do 10, maybe even 6-8!