IA32 IDT and linux interrupt handler

In the IDT each line has some bits called "DPL" - Descriptor Privileg Level, 0 for kernel and 3 for normal users(maybe there are more levels). I don't understand 2 things:

1. this is the level required to run the interrupt handler code? or to the trigger the event that leads to it?. because system_call has DPL=3, so in user-mode we can do "int 0x80". but in linux only the kernel handle interrupts, so we can trigger the event but not handle it? even though we have the right CPL.

2. In linux only the kernel handle interrupts, but when an interrupt(or trap) happens, what get us into the kernel mode?

Sorry for any mistakes, I am new to all this stuff and just trying to learn.