If the markers are white, they are probably something that is paint based or maybe white out. So, it'll take some sort of solvent to remove them. Just be really careful. It may be easier and safer to rub them off with steel wool or something. Have you tried to scratch them off with your fingernail?
"Lectric Shave" is pretty much alcohol and fragrance. Not good for a fb. It'll dry it out. There's no point in cleaning a fb at all really, but if you must, a VERY light amount of mineral oil or the like on a rag is probably best.
Cigarette smoke is much worse for you than it is the bass.

It'll just make it stink and over time give a nice, nasty yellow film all over. I don't think it will dry it out. It is a good idea to monitor the humidity though. The winter gets pretty dry in some places. Humidity levels below 30-35 are considered the danger zone for DBs. You can have things like seams splitting and even worse, tops cracking. Not fun.
Don't boil the strings. A lot of DB strings have things within the core besides metal to help dampen harsh overtones.