A transaction coordinator manages the administrative side of a deal from the moment the purchase contract is signed through to closing. That window is what people mean by "contract to close." You're tracking deadlines, collecting signatures, making sure the disclosures required in that state are delivered, chasing the lender and title company for status, and keeping every party told what happens next. You aren't negotiating and you aren't advising anyone on price or terms.
$350 per file sits inside the normal band. Most per-file fees land somewhere between $300 and $500, lower for simple cash deals, higher where the paperwork is heavy or the coordinator also handles listing setup. The fee is usually per file, not per side, so if you coordinate both sides of the same deal that's two files.
On licensing, both things you read describe real states. Requirements differ by state: some allow unlicensed people to do purely clerical coordination, some require a license or supervision by a sponsoring broker once you're doing anything that looks like advising on terms, and the line moves. Ask your state real estate commission and ask her broker in writing what they permit, because the broker's own policy is often stricter than the state rule.
The thing that will bite you first is when you get paid. If your fee comes out at closing and the deal dies during inspection, you've done three weeks of work for nothing. Decide now whether you charge a smaller non-refundable amount up front, or accept the fallout as a cost of doing business, and put it in your agreement with her either way.
