yes you can run the 12v led strip lights from your battery but i always recommend you use a fuse somewhere close to the battery is case you get a short.
what kind of control are you looking to get? a PLC will only give you on/off control where a RGB controller can give you full color control (if you are interested in the RGB strips)
http://www.instructables.com/id/LED-Deck-Lighting-in-color/ some pictures of the RGB strips installed under a deck railing
http://www.youtube.com/watch?v=seQzT6a75jA RGB strips in a boat
as far as supporting them i would zip tie them to a cable for support but for shorter runs you could hang them.
and yes as long as you use the IP-68 ones you should be fine