I have no experience with game consoles. My nephew is sending me an old Xbox console for my son from the US. Is it compatible with the PAL format here or incompatible with NTSC? Is there a country default setting? Can I plug it into any monitor or laptop, or do I need a TV?

Finally. This is a freebie, but what will it cost me in duty and taxes being shipped from the US? Should I just can the idea and buy a used one here?

Most of the TV's that you get out here are capable of world standard and will accept either PAL or NTSC (Multisystem)

you will need a TV. you could do it with a monitor but you may need some various cable adapters and speakers for sound.

You may need to purchase a new power brick to use with the Xbox. if it's coming from the US odds are that it's just 100-110 and not dual voltage.

Check the power brick VERY carefully when it arrives you could damage the system by plugging it in. if it does says 110-240 you're good to go.

The xbox has had several iterations over it's live cycle and not all power bricks are compatible with all counsels. if you require a new one I suggest taking the counsel into the shop and having the shop owner fit it/test it for you.

As regards customs it's anybody's guess. Might get away with it being free, might be 1-2K ???

Worst case is 30% import duty + 7%Vat on what they would determine is a new price for a new counsel.