I'm sure plenty of people DON'T ask for the health insurance information upfront, but there's no reason that you shouldn't. You don't have to divulge anything about
your health upfront either. If you're questioned, you can just say, "The health insurance is part of the compensation package so it's important for me to have a complete picture before I accept your offer." Look at it this way -- if the health insurance is $3000 more expensive than your current plan per year, or if it covers $3000 less per year, then that's the equivalent of taking a $3000 pay cut. An employer would never expect you to accept a job offer that said "We'll pay you $30,000 or $33,000 per year. You'll find out after you start." It sounds like you're a bit desperate to take this job offer... but there's no reason for them to know that
As AZYooper said, Remicade probably won't be on the prescript
ion drug list because it requires a "procedure" (IV infusion), not just a prescript
ion you can fill yourself at the pharmacy. Some insurance companies might have this info available online but I think most likely you will have to call them up on the phone to get the information you need.