1 - LIRR is a commuter parking lot, but you do not need any special permit
or sticker. as long as you park in a marked space you should be fine.
if you are parking for a long term, make sure you park near the station
platform/stairs since there are many people who work nights and weekend
park close too. Generally its a safe place to park a car.

2 - Town of Islip issues annual parking permits to residents for ISP.
they are I think $20/year
http://www.macarthurairport.com/pages/parking.shtml
If you qualify, its an excellent idea. Parking is not too far from the
terminal either.

3 - Yes, I've seen $5 taxi each way to ISP from Ronkonkoma station,
but I'm not sure what the other way around is like.

4 - Long term parking is not so bad at $11/day.