Does a TCP sender re-transmit the exact same SYN as the previous SYN after a timer expires?

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In case that a sender sent SYN at the first time, but the sender did not receive SYN/ACK in a timeout duration.

(Q1) When the sender retransmits SYN again, is the re-transmitted SYN same as the previous SYN?

(Q2) Are their sequence numbers same?

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Yes it does, but you might observe a difference or two.

A retransmission is exactly what it sounds like; the original packet is retransmitted. This means that the source host, source port, destination host, destination port, initial sequence number, etc. are all the same.

However, if the system supports PAWS and sends the TCP timestamp option, you should expect that the timestamp will change. As a result, the TCP checksum will also change.