I tried giving my monk two weapon fighting and ambidexterity but could not get him to dual wield his fists. Does it not work, or is there something I'm missing.

I thought about doing that as well but decided against it since the Monks hands are extensions of itself and not really weapons as such from the descriptions given of two weapon fighting and ambidexterity. As a result of my interpretation of the descriptions I decided against it but it would be good to get some clarification.

If you look at your monk in combat, you'll notice he only uses right hand to punch at enemies. which I suspect that two weapon fighting and ambidexterity does not work with his martial art. those two only works for weapon.

I give my monk a shield in one hand and just let him use the one hand to fight with. Though I don't know if shields disadvantage the monk like heavy armour does.

I think shields at least are supposed to disadvantage monks.

Monks' are using both hands, legs and whatnot, it's martial arts. However, as the devs didn't bother making lots'a new animations for monks (only other IE game they've been in is BG2, and there they were human only), they haven't got their own cool animations for their ass-kicking, and them fighting look sorta... not amazing.

Shields do limit the monk bonuses just like armor...
you can however have the monk use fist as main weopon and give some other weapon in offhand... this gives no penalties, just the standard dual wielding penalties

but in the character sheet it only list one damage only ( or two when you got really high level ) . I assume this damage comes from the right hand? if monks uses both hands and legs. we would able to see 4 damage in the charatcer sheet.