Suggested answer:
(1) The corpus results suggest that the expressions with the delexical verb take are most typically used in American English texts, while the expressions with delexical have are typically used in British English texts, e.g.:
I got to take a bath. (US)
...as soon as I got home I'd have to have a bath. (UK)
"Now, listen," I said, "take a shower." (US)

There were no occurrences of UK or US texts with the expression have a shower.

(2) On weekends and different than typically occur in US texts, while at weekends and different to typically occur in UK texts. Although different prepositions have been used in the two varieties, the meanings are the same. E.g.:
On weekends, J.D. came over and they talked. (US)
It's different than any of the other blood splatters on the car. (US)
... and only come home at weekends. (UK)
...Francesca did seem different to him... (UK)

(3) The search string already got yields examples of both the simple past vs. the present perfective, i.e. got is either the only verb in the VP (simple past) or it is part of a split VP (present perfective). E.g.:
I already got a house. (simple past) You've already got Oswin... (present perfective).

The pattern is quite clear in this case; the simple past is used in US texts in cases where UK texts prefer the present perfective.

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Read about grammatical differences between American and British English here
Terminology: delexical verb, present perfective, preposition