All of your sentences look good (except 1a), and have the same meaning between a/b.
Regarding 1a, since you are talking about only 1 family, you should use "eats". In 1b, you are talking about multiple members of a family, so you use "eat". For example:
The family eats.
The families eat.
A member of my family eats.
Members of my family eat.
The dog barks.
The dogs bark.