Signature in Ethereum: Are all a transaction fields signed?

Question

Assume a transaction is tx. My question is that

Question 1: Does a sender sign all fields in a transaction and put the signature in the transaction?, so does it send to the network?

Question 2: Is there anything in a transaction not signed by the sender?

Answer 1

The answers you seek are in the Yellow Paper, Appendix F and section 4.3.

Specifically,

This means that for a normal transaction (not contract creation) the following quantities are signed:

• The nonce
• The gas price
• The gas amount
• The To address
• The value
• The transaction data

(optionally a new signature scheme involving chainId is also allowed as described in EIP 155)

The only non-signed elements of the transaction are v, r and s, "Values corresponding to the signature of the transaction and used to determine the sender of the transaction" - i.e. the signature itself.