Easiest way to detect if there's an RFID tag is to put your shorts in the microwave for 10 seconds. Jokes aside, the only cases I know of where the RFID tag is sewn into the item permanently, is major Hotel chain towels.

Most likely it’s not NFC but a lower-frequency RFID (which as a side-effect gives it better range). You could use something like Proxmark3 (it’s an SDR and can speak many RFID standards in addition to NFC).

If the NFC tag hasn't been locked, yes. On android I suggest using NFCTools, it's pretty good and gives you a lot of room for playing