Can a quote change after I agree to it?
In short: Not without your agreement in writing. If the job turns out to be different from the scope (more cards, a different purpose), I tell you and re-quote before doing the extra work.
The fee in the engagement letter is the fee for the scope in the letter. Hourly work runs to the stated basis and minimum, and I tell you before a job is going to run long.
Cancelling before work begins costs nothing. If you cancel partway through, work already performed is billed at the stated basis, and nothing more.
A typical example
You ask for a written appraisal of a collection for insurance, and at the inspection there are more cards than the scope lists. I stop at the scope, tell you, and send a revised quote for the extra cards. Nothing is added to the invoice until you agree in writing.
Hourly work
Consults and claim work are hourly with a stated minimum. If a job is going to take longer than expected, I tell you before it runs over, so you can decide whether to continue. Payment is by invoice for the work the letter covers; see how do I pay?.