The BIOS sets up the interrupt environment like a PC BIOS on a 8088 would which has the least exceptions and already the AT with 80286 and added exceptions must be set up in a compatible way.

So on a 286 and later, it's not the job of the BIOS to handle exceptions, as they should not happen anyway in a way that the BIOS needs to hande them. 

If you are executing opcodes that do cause exceptions, your code is not any more compatible with BIOS or DOS and must know that you are running opcodes of 286 or higher CPU, which means you must already have detected the CPU and set up the environment that can handle the exceptions.

So the conflicts do not matter, as no code running properly under BIOS and DOS in real mode should not be able to trigger them.

For the INT5 which is the BIOS Print Screen interrupt triggered by BIOS keyboard hardware interrupt by pressing the Print Screen button, the BOUND exception will not trigger if you don't run the BOUND opcode. And if you do, your code must beforehand install a handler for that exception, which also means you need a custom keyboard handler which does not call INT5 when Print Screen is pressed.

For INT 9h, the BIOS uses it as keyboard interrupt. It does not expect it to be called as an exception if misaligned segment access happens, and BIOS handler will not try to detect if it was an exception or real keyboard interrupt. The program was misbehaving anyway.

Int 0cH and 0dH likewise, but only if the IRQ4 and IRQ5 are used by something. IRQ4 is very typical for serial mouse. And IRQ5 for hard disk BIOS. Parallel ports do not use IRQs under BIOS. IRQ5 could be free for a sound card, so a game handling the IRQ itself definitely does not expect CPU exceptions.

Likewise for the hardware IRQs 0..7 the BIOS sets up the vectors 8h..Fh. BIOS itself might only use timer IRQ 0, keyboard IRQ 1 and floppy IRQ 6, with XT era hard disk on IRQ 5. If any of those exceptions get triggered by opcodes you execute, that's bad news again, the BIOS handles the hardware IRQs, not the CPU exceptions. If you run code that requires these exceptions on a 286 or later CPU, your code is again not compatible with BIOS any more, and you need to reconfigure the hardware vectors to some other interrupts and run your own program/OS with drivers/code that replaces the BIOS functionality to access the hardware.

For 286 the reserved exception table covers the interrupts 00h..1Fh.

So basically, as per 286 documentation, the 286 or later CPUs should excecute correctly made 8088/8086 programs in a way that is compatible with BIOS. 

The added six exceptions only trigger if opcode was unknown, or there is a segment wraparound attempted. The other exceptions (BOUND, etc) should not happen as correctly running 8088/8086 code is not able to trigger them.

So only code that knows which CPU there is and can/will use the new exceptions is not compatible with real mode BIOS interface any more and must then also install the handlers for the exceptions it uses and use the hardware in other way than through BIOS.