Aside from the formal/informal distinction, there is a slightly different meaning between start and get started. At best, if being used to introduce something, the grammar would have to change a little, e.g Let's get started on building this table Let's start building this table Getting started implies a description of the process, get started is a suggestion to the reader to do so, obviously to be followed by instructions. Here, the meaning of 'get' is 'become', or 'be' in the transformative rather than durative sense
In your examples, 'this action got started' might be used especially in the us, but sounds unusual to british ears It would be the passive, meaning 'was started' You (had) better get started if you want to finish on time To begin an important period in one's life or career newlyweds who are just getting started on their lives together The form get started has the bare form of the verb get, used for present tense and as a bare infinitive (without to) The verb let's is a contraction of let.
From that point things started to getting complicated Which of these sentences would be correct, if i want to imply that something happened and things are not in order anymore? Is there any difference between these two sentences We're about to get started In let's get started, the starting point is in view and let's get going, you are on the starting point already Moreover, there is a sense of extra involvement abundantly made clear by the sentence, let's start going.
2 as you say, started is a past perfect participle which effectively is an adjective, the program is started It seems to me you can use the get + past perfect participle with any verb where the past perfect participle is a similarly idiomatic adjective We need to find a way to get them motivated You'd better leave before you get tired.
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