I don't know of independent security audits, but your questions 1-4 are relatively easily answered from official sources. I would have no reason to distrust the official sources on those matters. The quick answers are:
- Yes, the TPM is tamper-proof hardware which stores and protects your key.
- This is manufacturer dependent but most use an exponential backoff, e.g. 1st bad attempt locks for 1 min, then 2 mins, 4 mins, 8 mins, etc. more here
- Yes, the recovery key is your key, so you can recover in case the TPM fails. more here
- TPM 2.0 supports new algorithms and other improvements. I don't think the changes are fundamental. more here
Your question number 5 is much more interesting! TrueCrypt and BitLocker have very different safety profiles, and this is where we do have to question how much we can trust the TPM manufacturers.
TrueCrypt is as secure as your passphrase. If you use a weak passphrase, your encryption can be broken by brute force. If you use a strong passphrase then as far as anyone can tell (at least anyone who will speak in public) then your data is safe. There are a few caveats on this (cold boot, evil maid) but in the case that your computer is stolen while turned off, the data is very well secured.
BitLocker is as secure as your TPM. If you use a weak password, your data is still safe because the TPM enforces a lockout. However, if your TPM can be compromised then your data is at risk. It may be possible to compromise the TPM by techniques like shaving it open layer by layer and using a scanning-tunnelling electron microscope. However, a much more practical concern is law enforcement back doors. The TPM manufacturers probably have a back door they can use to get in, and they would likely reveal this to law enforcement in certain circumstances.
I can see why law enforcement would hate TrueCrypt! BitLocker gives adequate protection for commercial uses. And TrueCrypt is ideal for criminals.
Even if someone did an independent security audit, it wouldn't normally be possible to determine whether there was a manufacturer back door.