Malicious software and hardware in mouse?

Hello

I assume a mouse like Logitech G302 can hold some data? Since it autoruns software / driver, when you connect it.

1.
Can you transfer malicious software to a mouse like Logitech G302, and then use it to infect a computer with malicious software?

2.
Can you scan a mouse like Logitech G302 for malicious software etc.?

3.
Can hidden hardware in a mouse like Logitech G302 be used as cellular internet hub, and then “steal” / transfer data from the computer, without the user knowing?

I am not looking for guides / tips on how to do it.
Just wanna know if it possible, and if it is only something like the NSA could do.

Thank you