"2. Engine ID is (another number 3837004). How do I check to see if this is the original engine?"

3837004 = 1955-1957 car block

F723HE this code format was used from 1957 upwards
F = Flint, MI
7 =
23 =
HE = 4xxx series, or 31xx-39xx with RPO 227 (PCV system)
http://www.1954advance-design.com/chev-specs/1957-t-ser.pdf

You will need the block and head date casting codes for getting/confirming the year of those parts.
http://www.1954advance-design.com/Web%20images/casting-code-photos/codes-ser-nums.html