1- Your prayers are valid since you don’t have 100% certainty that the drop of moisture is urine. It may be urine or it may be residual moisture. If you apply these steps after urinating:
https://www.sistani.org/english/qa/01226/
Then you can consider the moisture pure. So don’t worry about previous prayers
2- You may consider them tahir since you don’t know 100% that it’s urine. Most washing machines purify the clothes if the machine pours plain water on the clothes at least twice
3- No need to keep a cloth close to it, because assuming urine actually out it made your body najes anyway…