In what ways are dice biased? Is the bias random?
For instance, am I more likely to roll a 2 than any other numbers on dice #1 and a 3 on dice #2?
You will never know unless you actually test for the bias, which essentially no one does.
Are all the dice from a particular batch or from a particular manufacturer biased towards a certain number? Or perhaps all the dice are biased in their own way? Imagine how cheaply most dice are mass produced? Expecting them to be free from bias is very naive. Even casino grade dice are going to have some intrinsic bias.
and the bias is random for each dice, wouldn't it even out if I have multiple dice (10, for instance) and roll them as many times as possible?
Again, you will never know unless you actually test your dice. Perhaps all 10 dice are biased to the same number, and so you are just compounding the problem rather than addressing it.
To take this further, how could someone take advantage of the bias in my dice to bruteforce my seed without knowing what that bias is?
If you produce a number with fewer bits of entropy then it is less secure, regardless of the bias which got you there.
As a way to mitigate bias, it's better to use different types of dice from different manufacturers, sizes, etc.
Maybe. A better option would be to test the dice first using a Chi squared test. A better still option would be to use a debiasing approach which guarantees a completely random result regardless of how biased your dice are.
When we are on the subject of manually testing a die, it's very difficult to discover a slight bias.
Correct, and actually it's impossible to prove there is no bias whatsoever. The best you can do is asymptotically 100% confidence, but you will never actually reach 100%. And as you want to become more and more sure, you need more and more rolls. You could rule out a 10% bias with a few dozen rolls, but to exclude a 1% bias you will need hundreds, if not thousands.