ok, thanks for your help and patience responding to my questions

I've ordered a cable to physically connect my speaker to the PI and will use that for sound in the future.

Next to mame2003, I can recommend its enhanced fork mame2003-plus and another arcade emulator called Final Burn Neo that is under ongoing development. But beware that every emulator needs its very own romset for the games to work, see Validating, Rebuilding, and Filtering Arcade ROMs.

Not currently, you need an SD card for boot.

You can store roms on the SSD though.

https://github.com/RetroPie/RetroPie-Setup/wiki/Running-ROMs-from-a-USB-drive

Have you tried to see if the cable is working - on another device ? Are you using a proper power source for your Pi ?
Unfortunately without a keyboard or without using SSH is going to be difficult to diagnose this. Is your Pi Zero the W model, with WiFi ?

@mitu

Thank you all for the help!!

ROM's are on my system, and it works perfect!

Next, I'll just need to hook the raspberry pie up via Ethernet cable to make sure it's updated.