I understand that the IY register is used by the TI-OS to address system flags and crucial for normal system operation, I also know that IY can be borrowed by the ASM programmer when necessary, provides it is eventually restored. But exactly WHEN is it safe to do so?

Do I need to just simply restoring IY before a system call? I wrote a program that saves and restores IY at the beginning/end of system call and execution, and program seems to work without problems, but I'm afraid of interrupts. Do system interrupts use IY? Should they be disabled during the entire duration when IY is being commandeered ?

Interrupts will be unaffected. You just need to restore it before certain system calls (the exact set that require it is not documented and subject to change, so you should just always do it).

Thanks.

This depends on if you are running on z80 or ez80 calculators. The z80 calculators will reset iy inside the interrupt handler, without saving it.