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Leaving the summons at a person's residence or where they have listed as their residence can be considered effective service of process. You don't have to actually hand it to the person in order for that to be legally acceptable. She could always go back to court later to challenge the effectiveness of the service of process, but getting a judgment overturned usually requires an additional ability to actually argue against the validity of the underlying claim itself.
The limitation in small claims on is the judgment, not what you can list as your claim. Sometimes, if I sue for $1000, the court might only find that I'm entitled to $800. So, if their total potential claim is $9750, they put that entire thing down in case the court decides that they aren't legally entitled to some of that amount. Regardless, the most the court would award in judgment is the judgment cap of $7500.
She can request a continuance based on her surgery if she can't make that date due to the medical issue. She needs to submit that request as quickly as possible, and certainly before the date of the hearing. She cannot use an attorney though on these facts. Attorneys are only permitted before a small claims court for very narrow circumstances (like the representation of a business, partnership, government agency, spouse or deployed military member). You could argue that her medical situation wouldn't let her present herself, but the court would likely just grant a continuance rather than allow attorney representation in that situation.
There is the Form for a delay or she can just walk into the county courthouse and ask their small claims clerk for a paper form to fill out.