See page 6 from Warn: https://www.warn.com/truck/winches/pdf/87968A2_rs.pdf
I wash the rope if it's really dirty. Other than that, I've only noticed light corrosion on the drum itself. Pretty easy to take care of.
Yes, a cover is a good idea imo.
Yep. Sun or snow. Here's a thread on covers: http://wayalife.com/showthread.php?31718-Winch-cover-options-advantages-disadvantages/page3
Post 22 is mine after driving through really snowy conditions.