Can I get just local anesthesia for my one upper wisdom tooth extraction? It's horizontal, impacted, but I absolutely do not want to be put to sleep.

Local Anesthesia. Many people have gotten their wisdom teeth removed with just local anesthesia. I'm sure you'll get through the procedure just fine.
Local anesthetic. Here should be no problem. Discuss the issue with your dentist or oral surgeon.
Yes. Usually not a problem especially if it isn't infected.