How common is it to get two urinary track infections in one month?

Recurrent UTI's. Recurrent urinary tract infections need to be evaluated and managed appropriately. You should see a urologist and have appropriate testing which will include urine testing and imaing of the urinary tract. Some patients may also need to undergo cystoscopy. Your urologist will determine the evaluation you needn and the results will guide treatment.
Depends. It's a tricky one. Although, anything is possible, there is a good chance that the "second" one is just the undertreated first. Often, empiric treatment prescribed for UTI may temporarily suppress the infection but not cure it. Occasionally a UTI may be caused by two or multiple bacteria and if treated without obtaining urine culture, may result in only partial improvement but eventual recurrence.