In Modern Warfare 3, for example if I am using a class that has the Support strike package and I get 2 kills and then die and change to a different class (also with a support strike package) will I still have a kill count of 2? If yes, do both classes need to be using exactly the same support set-up?
No, you lose your entire Support strike package pointstreak when you switch, even if you're switching to a class that has the exact same setup for its pointstreaks. I think this is just an intentional downside of switching classes with Support.
I used to have an "anti-air" class that I'd switch to with a launcher secondary for times when we were getting overwhelmed by air support. However, with this restriction, I usually just don't switch, or set up a class that has aspects of both my normal and anti-air class together.