You can also catch buses to KBP although, i don't seem to remember the bus numbers.
The tram route to Bronowice should pass closer to KBP, i would have thought. I'm not entirely sure but may be someone on here is more informed than i am, my info could be entirely outdated (last used MPK krakow in 2008).
Yep, basically train and car. Both are strugle, but I'd choose the train from the main central station. Goes 15 min. to KBP, ticket is around 2.5 PLN and you dont need to look for a parking space which is scarce at KBP at the moment.