The Separated by a Common Language blog, by a University of Sussex linguist, offers a quick overview of do you have versus have you got for asking about possession. A search on corpora returned these frequencies:
AmE: Do you have = 3092, Have you got = 99. So 31:1.
BrE: Do you have = 245, Have you got = 450. So 1:<2.
In summary, she concludes
If you are on a UK street corner, say Have you got a pineapple?
If you are on a US street corner, say Do you have a pineapple?
If you say Have you a pineapple?, you risk assault for non-normative behavio(u)r.
Separately, it's not clear what your example sentences mean. As noted in Do you have a / the time?, if you mean you are unaware of the time of day, you would say the time as another answer has indicated. It can also be used if referring to some known block of time, e.g. I don't have the time to discuss this at the moment. But the zero article can be appropriate if referring to time as an uncountable property, thus I don't have time to discuss this at the moment.
1 "I haven't had a talk with her in a very long time.
2 I haven't had a talk with her a very long time.
3 I haven't had a talk with her for a very long time.
"Are all the above sentences grammatically correct? What's the difference in their meaning?"
In the above examples, numbers 1 and 3 are grammatically correct and have no difference in meaning. Number 2 is incorrect because it is missing a preposition to link "a very long time" with "I haven't had a talk with her."
Your sentence provides three pieces of information.
Event 1: I got home
Event 2: he arrived
Timeline: 2 occurred before 1.
Without further information from the context, you cannot infer that he was there when you arrived: you cannot even infer that he arrived at your house- he could have arrived somewhere different.
Best Answer
Have and have got (and have gotten) are used differently in British English and American English— in fact, it is one of the key distinctions between the two, though the American forms have reportedly become more common in the UK. Some examination is covered in What do "have", "get" and "got" mean? as well as What do you have to say for yourself? / What have you got to say for yourself? . Also see at EL&U, “have” vs.“have got” in American and British English and many others.
The Separated by a Common Language blog, by a University of Sussex linguist, offers a quick overview of do you have versus have you got for asking about possession. A search on corpora returned these frequencies:
In summary, she concludes
Separately, it's not clear what your example sentences mean. As noted in Do you have a / the time?, if you mean you are unaware of the time of day, you would say the time as another answer has indicated. It can also be used if referring to some known block of time, e.g. I don't have the time to discuss this at the moment. But the zero article can be appropriate if referring to time as an uncountable property, thus I don't have time to discuss this at the moment.