It's been my experience (over nearly 40 years) that indeed, in dry weather, you don't need to apply any creams or ointments to a synthetic chamois (you must ALWAYS apply some ointment to a real chamois!), but if you are riding in the rain without fenders, it's a good idea to put something on the synthetic; otherwise, your butt will get burned by the friction. Something about really wet synthetic chamois is not good for the skin.
If it's a real chamois, you always put some sort of ointment on it (I used to use a Dutch product called Jecovitol, made from fish oil that was heavily perfumed and had quite a nice aroma until the perfume wore off, and then it smelled just awful, but the shorts would be ready for a wash anyway; my first track coach, a former pro 6-day racer, had us use this stuff.). The reason for this is pretty obvious if you have ever washed a real chamois. Once it dries, it's all bend and twisted and feels like cardboard. You have to rub it against itself to loosen it up, and then you have to moisten it with some ointment because you don't want this rough cardboard chafing against your skin! Thank god for synthetic chamois!
As far as getting it clean, just dump the shorts in the wash with the other dark fabrics! But I hang all my cycling clothes to dry, though.
L.