MacOS – Genius external keyboard working improperly on Macbook Pro

I answered a similar question several months ago, the answer is somewhat applicable here as well.

Try this...

• Power on your Mac while holding the option key on your keyboard. If done correctly, and assuming a firmware password is not set, you should see your internal hard drive show up on the display. If you DO have a firmware password set then you will be prompted to enter the password before moving on. This is just to verify what you should see.

If you don't see these screens then your key is likely failed at the hardware level. If this is the case then you have to replace the entire top case since the keyboard is built into this component. If the key had popped off you could replace just the key but any sort of functional (non cosmetic) repair requires the keyboard be replaced. The repair for this isn't terribly difficult although it is somewhat involved since the top case is basically the chassis that everything bolts to, meaning you have to tear the MacBook Pro down completely in the process. iFixit has a great guide (and possibly a replacement part) that shows the process.

If you see what I describe above then your key is functioning properly at the hardware level and the issue instead rests somewhere in your operating system. To narrow down the issue I would create a test user account (or just enable and login to the Guest user) to see if the issue persisted when logged in as the test user. If the issue persists for the test user then it's a system wide issue, if it doesn't then it's something in your ~/Library folder. If that didn't do the trick I would use Disk Utility to repair permissions, verify and repair the disk. If need be I would reinstall the operating system, without first erasing the disk assuming you have data you'd like to preserve.

Hopefully that puts you in the right direction, good luck!

Then, it asks to press the key on the left of right shift. When I press 'Z' key three times

Z is on the right of the left Shift key. You sure you pressing the right keys? According to your post you should be pressing the "/" key.