RFID/NFC (13.56 MHz), is it possible to send raw bytes and receive response? I'm trying to implement a card reader (i.e. credit cards) for shopping purposes, and AFAIK those cards are ISO 14443-A compliant (Mifare Classic 1K). I already made an Android app that can send custom APDU to read specific sectors by using raw SendBytes().

Since I need to build a circuit with a custom antenna, I chose Arduino-uno with a NFC module (was thinking about StrongLink SL013), I wanted to know if it's possible to send raw bytes and receive the response from the tag. I only found some higher-level implementation (readSector, writeSector and so on).
RFID protocols require either passive or active tags.  Depending on which you use, either the tag or reader regularly transmits pulses.  Check www.rfidreader.com for more info.  https://www.rfidjournal.com provides valuable resources as well.

Many companies invest heavily in developing RFID technology.  You would be well advised not to reinvent wheels without reeeeally deeeeeep pockets.