1) I have used dbPowerAmp and it is very useful.
http://www.dbpoweramp.com/
2) If you are going to use WMA, Windows Media Player is probably your best (and maybe only) option. There aren't a lot of 3rd party applications that have WMA support.
3) You can 'toggle' the screen in Tools>Settings>Buttons in WMP and similarly in other music players like GSPlayer which may be the most popular 3rd party (freeware) player out there.
4) Though this topic has been debated, many use Ogg format because it tends to be smaller at similar quality levels. Most of this will be determined by your tolerance for music 'quality.' I would suggest that you convert into a few different formats and test them out. I use Ogg almost exclusively with GsPlayer. You can check out GsPlayer at this website...
http://hp.vector.co.jp/authors/VA032810/
I hope this helps you out somewhat. I would do a search for similar topics and check out the multimedia forum for more in depth answers.
Have fun listening!