You can app to as many people as you want within 14 days for the same type of loan and have it only count as one inquiry.
Buy NOTHING extra. Check with you Insurance carrier to see if they offer GAP Insurance (you MUST have this) As long as your insurance carrier offers GAP insurance with no limit then it will be cheaper to buy through them (My last car it would have cost me $600 dollors for 72 months, thru my Insurance it is $11 for every 6 months)
An extended warranty can always be purchased at the end of the Factory Warranty so you do not want to finance that. Rustproofing, paint protectant, desert packages, winter packages etc. are all put on at the factory not added once the car is received at the dealership (but they they tell you it is). They always talk by saying for only $11 more you get xyz, but that is $11 per monthly payment and not worth it.
Good Luck!