'Get' + past participle is an alternative to 'Be'+ past participle in some - but not all - uses of the passive. We often use it for negative outcomes eg my house got burgled, the policeman got shot, John got fired from his job. It's also used to suggest a degree of difficulty eg after a number of problems the hotel finally got built. It's tricky to know when it's appropriate to use a 'get' passive and when it isn't. From your point of view, it's probably be best to be aware of this form, but stick to to the standard 'be' passive in most cases. You should also remember that all sentences with 'get' tend to be more informal than their equivalents without 'that'.

No, the meaning does not change. For some common expressions, we prefer one over the other, but they have the same meaning.