3. After dinner we visited Martha and her new baby
is it a direct object or a predicate nouns?

"The car is a Toyota."
"The lake was a tranquil pool of beauty."

'Toyota' is a predicate noun, coming after a linking verb. 'Toyota' links to 'car' and tells us about the car.
Similarly, 'lake' and 'tranquil pool'.

In your sentence, 'we', 'Martha' and 'baby' are separate persons.

"Martha and her new baby' is the direct object of the sentence.