Hi! I am reading about segwit and I have several questions about it.

1) I've read that a segwit transaction cannot spend non-segwit utxos. Is this correct? How can you then create your first segwit transaction, if you only have non-segwit utxos? I am sure I am missing something there.
2) Is the new segwit serialization format really backwards compatible? I have been looking at it and I am pretty sure that wallets that do not understand segwit will not be able to recognize a segwit transaction, and thus, they might think that the block is invalid for including non-standard transactions?
3) I also read that there will now be two ways of identifying transactions, the txid (which is the hash of the transaction serialized the old way) and the wtxid (the hash of the transaction serialized as segwit). When signing the transactions, do you also use the old serialization to calculate the hash you need to sign? or do you serialize it as segwit? (in which case, again, old wallets would not be able to verify the signature).
4) If the txid included in the merkle tree is not the wtxid, then, how can you tell if a transaction is segwit or not when it is presented to you using the old serialization?

Thanks a lot in advance!