I've been tasked to write and read data to this card. Vendor gave me Intelligent Tablet Payment Terminal i9300 and expect to write and read data to this card below. Intelligent Tablet Payment Terminal i9300 is Android based. It comes with its own SDK which poorly documented. What card is this and how do I even begin?
Yes it is an RFID card.
A lot of information can be derived from the documentation of the terminal you specified Intelligent Tablet Payment Terminal i9300.
You can read more on RFID read/write at How can I write data on UHF RFID tags? and Can I write or modify data on an RFID tag?
You can sort-out your basic RFID queries from How do RFID systems work? and RFID Journal