2.1 - Yes, with a slightly different meaning,2. Can we rewrite the sentences to -that clauses?
2.1) Fortunately, I passed the test. -> it was fortunate that I passed the test.
2.2) Increasingly, they distrust the government. -> it is increasing that they do not trust the government.
2.2 - NoThere could be.3. Do you sense any difference between 2.2) and 3.1)
3.1) They increasingly distrust the government.