Does a blockchain become opaque if it enable's schnorr-signatures, and require trust in the code? When you sign a transaction with schnorr-signatures, it does not include the pubkey in the transaction data. 

1)Does this mean the input addresses become unknown, aka creating a opaque blockchain ?       

2) How can one make sure that for example bitcoin still only has 21 million bitcoins ?     

3) How does the UTXO set updated and than later on verified by others, seeing only the output address is know.
When you sign a transaction with schnorr-signatures, it does not include the pubkey in the transaction data.


What? Schnorr signature validation still need public keys.


  1)Does this mean the input addresses become unknown, aka creating a opaque blockchain ?


No, there are still addresses just like before (or more technically: every input still explicitly refers to a single identifiable previous output which is being spent in its entirety)


  2) How can one make sure that for example bitcoin still only has 21 million bitcoins ?


By summing up the value of all UTXOs.


  3) How does the UTXO set updated and than later on verified by others, seeing only the output address is know.


Nothing is changed. The UTXO set still contains entries, each of which has a txid, amount, and scriptPubKey. Now you just need a Schnorr signature to spend them.