Exactly the point. If you have no idea how biased your dice are, then why would you feel comfortable using them to generate something as sensitive as a bitcoin private key or seed phrase? That's just irresponsible.

Depends how certain you want to be that your coin is fair. You can never be 100% sure your coin is fair, but you can asymptotically approach 100% with increasing confidence of ruling out ever smaller biases. For example, to exclude a 55/45 bias with 99% confidence, you would need to flip the coin 664 times. However, to exclude a 51/49 bias with 99% confidence, you would need to flip the coin 16,589 times.

A more practical approach would be to simply us the von Neumann approach I alluded to above. Take any coin and start flipping it in twice. If the first flip is heads and the second flip is tails, write down 0. If the first flip is tails and the second flip is heads, write down 1. If the two flips are both heads or both tails, don't write down anything. Repeat until you have 128 zeros or ones written down. This method completely eliminates any bias in the coin and produces a uniformly distributed output. It will require a lot less flips than any method to test whether or not your coin is actually fair.