Can I use "have got" like those?
My mother wants to have got a child (or) My mother wants to have a child.
He may/might/could/can/should (modal verbs) have got a car (or) he (modal verbs) have a car.
Can I use "have got" in future form?
I think "have got" can be used in past tense, except Progressive,past perf,present perf,and future tense.
E.g. He had got a motorcycle / he had a motorcycle.
He has got a red apple / He has a red apple.
*He will have got a dog/He is having got a dog/he has had got a dog/ he had had got a dog. *
The correct are : he will have a dog/he is having a dog/he has had a dog/ he had had a dog.