If a client does not physically sign a contract but verbally agrees to it and pays the full amount, are they still obligated to follow the terms if they cancel services?

Even though she did not sign the contract, a court would most likely find that an enforceable contract exists and she is obligated to it: you sent her the contract, which means you offered her certain terms; she showed that she accepted or agreed to those terms, by making payments under the contract, doing necessary planning (the timeline) needed for the contract, sent texts agreeing to or referencing the contract, stated orally that she agreed to it, etc.; and as stated, she provided consideration (made payments) and you, too, provided consideration (hired an assistant; reserved the day for her)--consideration is either giving the other side side something of value (which includes valuable promises--like reserving the day for her) or expending money, effort, time, etc. in furtherance of the contract (hiring the assistant).
When you have an offer, evidence of acceptance of that offer, and an exchange of consideration, you have a contract, even if the other side did not necessarily sign on the bottom line.
Therefore, you can hold her to the terms of the contract, suchs no refund; can sue her for any additional amounts due; and if she gives you a bad review which contains *lies,* you could sue her for defamation. But only if the review has factual untruths. So if she writes that you illegally kept her money, you could sue--you seem, as discussed above, to be legally entitled to it. But if she wrote that you were greedy and unreasonable and refused to refund the money to her when she told you she wanted to cancel 2 months in advance, that is either her opinion ("greedy" and "unreasonable" are opinions, not facts) or is a true fact (you write she did try to cancel 2 months in advance); but neither opinions nor true facts are defamation, so in this case, you could not sue.