“Can anxiety be cured completely?”

Yes, most types of anxiety can be cured. The main exception is Obsessive Compulsive Disorder (OCD), which can be significantly improved, but usually cannot be cured. All of the other types of anxiety have a type of psychotherapy that is effective at curing it although it can take several years. Medication mostly just relieves the symptoms while you take it, but doesn't directly promote a cure. Traumatic anxiety and phobias are exceptions to the "meds just help symptoms" rule. There are some blood pressure medications that actually seem to promote the cure when used with psychotherapy. A better way to think about medication for anxiety is to think of medication as being able to decrease your anxiety so you are not overwhelmed and can focus on doing the therapy that will eventually cure you.
I hope this helps.

Yes, I believe so.