If you take one dose of xanax (alprazolam) every other day, or every 2 days, will physical dependency occur? or will skipping 1-2 days prevent dependency?

Will not occur: Physical dependency to most sedative-hypnotic drugs, including alprazolam and alcohol, usually requires either very high dose use on a binge basis, or regular use of the medication multiple times per day for a fixed amount of time (usually at least several weeks). Taking Xanax in a single dose (as long as that is a therapeutic dose), particularly every other day, will not usually cause dependency.