Why does my keyboard type < after I press a?

Try the USB keyboard on another device. If it does the same thing there, the keyboard itself is the likely culprit. If it works normally, look at settings, remapping software and drivers on the laptop.

You could also try a text field in the BIOS or UEFI setup, if yours has one. A problem there points away from software running in your usual operating system, though it doesn't prove exactly which hardware component is at fault.

The Ctrl and z behavior sounds like Ctrl might be acting as Backspace, making z behave like an undo shortcut. That could happen if the keyboard is sending extra or incorrect key signals. A keyboard event viewer can help show which keys the computer thinks you're pressing.

Check for key remaps or macros, especially if the keyboard has configuration software or onboard profiles. A macro can make one key send several characters. That said, the other odd keys make a keyboard fault worth checking too.

If the issue follows the keyboard to another device, a short or contamination inside it is possible, even without a known spill. Unplug it and check for debris or moisture. If it's an inexpensive office keyboard, replacing it may be less hassle than opening and cleaning it.