yes.
Depends on what your burner supports--if it supports -r, you need -r, if it needs +r, you need +r. If it supports both, then it depends on where you are trying to view it. Generally speaking, -r is more compatible, but some standalones prefer +r.
All things being equal, -r is probably more compatible and is cheaper and can commonly burn faster.
you don't have to. They may play in your standalone or whereever else you want to play them. You can check standalone compatibility at
http://www.dvdrhelp.com/dvdplayers.php
Use -R media, +R are more likely to not be supported from a DVD player and they are not the official blank DVD format supported by the DVD Forum (this is DVD-R).
The 90% of the players will work with -R, while just a 70% of the players will play +R. Especially the older players that do not support DVD writable discs at all may play with DVD-R.
Note that there are even computer DVD readers that cannot read DVD+R.