Been taking. 5mg of Xanax (alprazolam) twice a day for one week. Am I addicted at this point?

Not necessarily. Just because you have been taking Xanax (alprazolam) for a week doesn't mean you are addicted. Addiction is when someone becomes depdent on the drug, physically and/or psychologically. When you are addicted, you may develop tolerance to the drug, may require higher and higher doses, withdraw if stopped, and misuse the drug to get the effect you want even if the use is compromising your daily function.
Up to two weeks ok. Addiction is a behavior. If you cannot stop using it you are addicted. May be your question is if you are going to experience withdrawal symptoms if you suddenly stop using it. Two weeks of using it is safe to stop otherwise look for help.
No. Xanax (alprazolam) needs to be taken at much higher dosages, for a much longer period of time, to require weaning due to addiction. I would suggest limiting the dosage to the minimum that is effective, and work on the underlying issues that are causing you to take this medication. You are better off to determine the cause of your anxiety issues, and deal with them with resolution in mind. This is the priority.