Convert serial read char to HEX and write to EEPROM

Don't confuse yourself to much with dec, hex, binary. That's just a representation for us humans. The Micrcontroller handles bits and bytes (let's say it works binary internally).

I suggest you follow the

Serial Input Basics - updated - Using Arduino / Introductory Tutorials - Arduino Forum

You end your string with the end tag #.
You save your buffer to a start address in the EEPROM with .put

Start with the Serial input basics. I will check later in the night your next try.