Freelance colorist, here - I'll see if I can't help you out.
Cost:
Cost is pretty dependent on the artist, as you likely already know, and what it includes is also going to depend on the artist. For me, I charge anywhere from $20/page to $45/page, depending on how soon you need the pages done, how detailed you need the coloring, etc. The best thing to do when figuring out where that leaves you in webcomic format, just ask the artist about charging per panel - for me, that would translate to about $4/panel to $9/panel. The lower end will get you some nice flats, and the upper end is more for full airbrushed rendering.
How long?:
Pretty artist dependent. Depending on how much time I have and my deadline, I can usually turn out a batch of flats (about 3 pages, or about 15 panels) in a day or so.
How/When does the artist typically get paid?:
Also artist dependent, but for myself and a lot of artists I know, I usually ask for half up front, half upon delivery. I've had too many clients ghost me while doing their work without ever getting paid for it - the down payment tells me that you're serious about this, and that it isn't going to be a waste of my time to do your project over someone else's project.
Hope that helped!