AFMCan LIBOR be negative?

It could be theoretically but unlikely in an examination setting.

LIBOR should be fixed. Maybe you mean like "LIBOR - x%"?

LIBOR is variable, fluctuating from time to time. LIBOR plus reflects the premium for additional risk.

In theory it could be negative, but in practice no.

LIBOR is inter bank interest rate..so it can never be negative..bank cannot charge negative interest to other bank....

In theory the bank could, but (as you say) in practice no.

If it is negative, then the lender will pay interest to the borrower?

I dont think LIBOR would be negative in theory as well, if it is negative it should be given other name so that we dont conflict with actual meaning of LIBOR. For example practically cash cannot be negative..and theoritically instead of saying negative cash we call it as bank overdraft..which is logical..
so i think negative LIBOR should be given some other name like LIBBR(London inter bank bid rate).