All sounds pretty regular. 35% is normal for art reps .As mentioned, there is a subtle distintion between “art rep” and “agent”, and an agent normally takes much less (15% is typical) but does not seek any work outside of publishing. Now, since it seems they also specialize in publishing, that is a bit confusing. There is much more jobs outside of publishing for an illustrator - how about those? They would not rep any of that? One important step is to get a full list of all the things they do rep for and those they don’t. If they really only rep for publishing, you should consider getting a literary agent instead - a majority of them has a mixed list nowadays, with writers AND illustrators. My agent is also fine with contracts that involve no royalties - but I have to admit that she does not focus a lot on usage rights - so maybe a rep specializing in illustration would have a keener eye on that kind of things.
Publishing is not a black-and-white definition either. Is it only books? Or also apps and software? How about e-books? Board games? Do they take a cut on all royalties and collaterals too? What if the company you end up working for does work that falls into their area of representation? Remember that an agent/rep will take their percentage on ANY job you do, no matter if it came through their mediation or not. Another item to discuss is for how long they will still take the cut after the contract is terminated - there is always a grace time and in the publishing industry this can be very long (because the industry is super slow). It may be up to a year after termination before you are actually “free”.
You can discuss anything with them beforehand - arrange a call if you haven’t done so already and don’t be afraid to question anything and everything. This is a business relationship and needs to be advantageous for both sides.
As @SarahLuAnn said, a good rep or agent can be totally worth their commission. I’m not always happy with my agent, but she is a great negotiatior and always gets considerably more money than I would have dreamed of asking. This is great at the beginning, when you’re not sure of your value. Also a good agent is in for the long haul and will be concerned with your reputation, career and workload management - that is precious guidance when you’re new to the business of illustration!