Usually its the 2nd. son who is named after the wife's father.
A ship that left from Liverpool, UK to New York would stop in Irish ports, Dublin, perhaps Wexford and Cork ports before crossing to New York. It would still be listed as leaving from Liverpool-NY.
That is very early for a woman to be having a child, although the average is 20, there must
be some in the lower range for 20 to be average.
Civil registration deaths usually give a year of birth on a death certificate as an estimate based on age given at death - not necessarily correct.
If the children were born in the UK try: www.freebmd.org.uk
also has marriages and deaths