In the US, we'd use "gotten" not "got". Samuel has explained the difference in meaning.

Yes they're fine I believe! The 'Did you get..' sentences refer to the past, whereas, the 'Have you got..' is what you would likely say in the present! For example, you would likely say "Did you get used to being rich?" to a former billionaire who is talking about their past. Conversely, you may say "Have you got used to being rich?" to a person who has just become a billionaire. I hope this helps!