I can actually answer your questions fairly accurately because of personal experience (I am NOT a lawyer, this is not legal advice). First of all, DE does not consider the income of the new spouse (you). They use the Melson formula (google for delaware melson formula and you will find an online calculator). With seven kids, this will be substantial! They DO garnish paychecks, I think it is automatic. As far as whether or not she works, I believe they do expect both spouses to work, but with seven kids, the childcare costs (which are considered on the Melson!) might be more than the ex makes, although you haven't said how old the kids are and whether or not the older ones babysitting can partially help out.
Medical expenses are also divided between the parents according to a percentage figured out by the melson. I think ordinarily the custodial parent has to pay the first $350, and then the remaining expenses are divided and the NCP has to pay his/her share within a "reasonable time". Things like summer camp (unless child is under 13 and it is childcare so parent can work), dance lessons, college, cars, etc are NOT included in Melson. Child support ends when child turns 18 AND graduates from HS,or when child turns 19 with or without graduation, but NCP has to file to kick kid off.
Typically this process starts with a hearing with a mediator, and if the parties don't agree, it goes before a commissioner whose decision is probably binding.
Best advice for boyfriend--get a lawyer, and be prepared at hearing with last 3 pay stubs, W2, tax returns, and anything else on the hearing notice. Be objective, don't lose temper. Do the Melson in advance so he knows what to expect. And, if you are marrying a man with seven kids, expect that he will have a very very substantial financial obligation to those children for a long time, and it shouldn't end when they turn 18. When you marry a man, you marry his children too. Think long and hard if you are going to resent him helping out those children into adulthood, not just during CS years, and if you think you are, then reconsider the relationship NOW!
Parents can agree on whatever they want to agree on with the mediator. If he and his ex agree that he will pay $50/month and they both sign off, the mediator probably won't object. Likewise, if they agree on $5000/month same deal.
Having said all that, my ex is a Delaware deadbeat dad who has gone to every CS hearing whining about how poor he is and how he is about to lose his house. I cave and let things go, and then he goes out and has a spending spree afterwards. At the moment he hasn't paid for 10 months because he got pensioned off from his job and they don't seem to be able to garnish his pension. He pays a pittance but even that is too much for him, because he is too busy supporting his sweetie and her kids (no offense to you). My ex left me to pay for college & medicals for our son who is now 21--his mantra "I don't have to pay for this so I won't!". Our 16 yr old has numerous mental health and learning disabilities and he hasn't lifted a finger to help. I've paid for summer camps, private tutoring, various fitness/activity lessons (she is also morbidly obese), riding lessons, and even her cell phone, all with not a penny from him. Now that DE is about to pull his drivers license, he's sucking up to the kid and is going for custody. Until now he has done ZERO for her!