What exactly does zram do and should I get rid of my swap?

Think of zram as a way for your system to juggle memory better. It lets you keep more stuff active without crashing, because it compresses information on the fly. You could delete your swap if you're confident, but I'd suggest keeping it until you're sure zram is doing the trick for you.

Zram is like creating a virtual memory area in your RAM itself, which helps speed up things by compressing the data. This means that instead of waiting for slow disk swap to kick in, your system can use this fast compressed memory. As for your swap partition, you might not need it as much now, but keeping it around can be a safety net in case you run out of RAM.