Read some (unknown?) RFID tags with a chinese reader / writer (125kHZ)
Since the reader actually works on the serial interface you will probably need the communication protocol and that is usually something you can't easily reverse engineer, but if you plan on the first thing you need to do is get it to respond and react in some way. You will probably not get it to do so by just sending random data to it, since it will interpret it as garbage and simply ignoring it. 
The only reliable step you can take is trying to find more information about the reader starting with the RFID chip, the store you bought it from, etc.
Searching the internet this seems to be more or less your reader:
RFID Reader

For the bonus question there is no way to know for sure without information directly printed on the tags, but you can restrict the range by excluding some uncommon types from the format of your tags. Given this:
1. The key-fob tag can either be a 125 kHz or 13.56 MHz;
2. Clam shell cards often come at 125 kHz, 13.56 MHz or 433 MHz;
3. The blank card can either be 125 kHz, 13.56 MHz, UHF EPC Gen 2 (860 - 960 MHz). Rarely I have seen 433 MHz cards like this.
4. I do not know about the key tag. If you could provide more information about it (what is it supposed to do).

From my knowledge there is no single reader which can read all these frequencies, the safest bet is one reader per frequency.