For verbs having 2 objects.... Can't use it only with 1 object ?

Please look at the following sentences first.
1] Where did you put my wallet on ? - I already gave it
2] Who did you give my wallet to ? - I already gave your mother
3] I already informed the news. / I already informed him.

Both "inform" and "give" are the verbs which have two objects.
I think I heard sometimes you, English or American is speaking like having only 1 object.
Now what I want to know is whether what I certainly heard like that is right or not.

Are all of the sentences in the above possible in grammar ?
I mean, do I have to say it with 2 objects in any case as " I already gave your mother that " or " I already informed him of the news like this ?

Q1)
Can I make a short answer as "I already gave your mother" since the asker has made an question for who ? so I think I can simply out on person only. Am I wrong ?

Q2)
If I can, okay, then for another thing, is it should be " I already gave your mother" or "I already gave to your mother" ? I'm confused on whether or not putting "to" in front of "person" ?

Thank you for your answers in advance.