Which is better, a weapon and a shield, or dual wielding two weapons?
Classically, dual wielding was better. The addition to AV has changed this fact. At this point, it's hard to say; the newer versions are not as well explored. That said: it probably depends on the specific weapons and shield. I've had some good success with sword-and-board style characters recently...
Is it better to wield a broken shield with higher AV, or an intact shield with lesser av?
As fejoa mentioned, a lighter, intact shield is probably better. In addition to the AV bonus, shields also have quite high block chance and block power. You lose a lot of both with a broken shield. If you can trade in a point of AV for an intact shield, I'd say it's worth it. Unless the new shield is made out of something absurd, like gold or silver. Weight impacts accuracy; accuracy impacts block chance.
To be precise: Blocking is dependent on a few things. The two which are relevant for your chance
to block (or, BlockValue) are accuracy and BlockModifier. BlockModifier value depends on the shape and size of the object; in addition, shields get a bonus x2 to BlockModifier that other items do not get. A broken shield has 2/3 the BlockModifier of an intact shield (size is reduced from 60 to 40 in broken state). Meanwhile, while I assume AV is applicable to every
attack, AV only mitigates between half and full AV in damage points - so, that shield currently mitigates on average 3 points of damage. A block can reduce damage by ... an amount that I and others spent significant time trying to work out a useable formula for, but even with a wooden shield a block can reliably negate most attacks in the UT (in my experience).
If you're curious, this thread
from 2016 includes a list of BlockValues for all items in 0.50, while this thread
from 2011 carries several attempts to break down the formula for BlockStrength which met with mixed success.
Any tips to improve this character's survival in his next goal will be appreciated.
Discretion is the better part of valor.