I don't know if you should spend time making an enclosure for coaxils. Most of them are designed for the general publics needs. examples: Good in free air, good off axis response.
No you don't have to seal up your basic speaker in a box. But you will need to run them IB = Infinite baffle as CJ mentioned. So sticking them in your doors or rear deck are a good idea. You can't just have them sitting on the floor...
EDIT - The reason you want to run them IB is to seperate the front and rear waves. If you want any midbass responce at all it is required. And It will keep it from sounding like poo
run them infinite baffle, meaning in a door or in the rear deck... dont be like the guy I saw today who couldnt install his pioneer coax's in his rear deck so he just taped them to the rear deck, aimed at the front.
Depends on the speaker. You can't make blanket statements like that.
Most car audio speakers are designed to work infinite baffle.....which means if you put them in an enclosure you will suffer some pretty unsettling consequences that will not please you sound wise.