Does the year of publishing for corrected proofs change in the final version?
Re. 1 - Yes. I have a paper that was published "epub ahead of print" in one year, and later published normally the next year. Both versions have different year numbers when cited.

Re. 2 - I would expect they do it in chronological order normally, but sometimes journals publish "special issues" on a specific topic that result in postponed or quicker printed versions. Also comments/replies to specific papers often get published in the same issue, suggesting that those ended up in print version quicker.