Your examples 1 & 2, a & b, are examples of the infinitive and the gerund used as nouns; this has no relation to the problem at hand. Get + sth + full infinitive is one of a group of causative verbs that take the ' to ' infinitive (there are other causatives that take the bare infinitive, like have sth do, let sth do . Others in the get group are cause sth to and force sth to.
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