I'm really sorry you're having to go through this, after believing that you were on track.
To play devil's advocate, I'm wondering if your preceptor thought each error was an isolated situation at the time, but as the time drew nearer she had a rethink. Your GPA, honour society status, etc really has no bearing on your clinical skills.
You say you overrode the system to give the patient his Flonase, not realizing it was not the proper time for administration. While the error itself is minor, it is important to acknowledge that you had no good rationale for overriding the system and you did not adhere to the 5 rights. (There have been recent lengthy threads about this very situation.)
When placing the Foley, you said you needed frequent intervention to keep from breaking sterility. Have you shown better proficiency since then? If so, mention in your appeal that you are a lot more competent in maintaining sterility. If your preceptor has reasons to still believe you haven't grasped the principles of sterile technique, that could be a concern.
No matter how non-cognitively intact you believe your patient to be, always give them the benefit of the doubt. That means you explain everything as you do it, as a matter of respect. Let the appeals committee know that you were very anxious placing a Foley for the first time and missed this and feel horrible that you forgot to treat the patient with basic respect.
It probably wouldn't hurt to mention that you were graded well each week(do you have copies of those weekly evaluations?)and felt confident that you were learning from your mistakes and that you are now dumbfounded at being told you are not ready to graduate.