Interesting! IMHO, the token should print as-is, unless you have them in different timezones than you want! The Last Interesting Moment Date, similar to other interesting moment standard fields, is a system-managed standard field that should ideally get updated by the system and should be pulled as-is when referenced via its token. I'd check with support if you keep seeing discrepancies in the data you see on the person info in the DB and in the email when referenced via the token (given that you have verified the potential difference due to timezones- i.e., the date time being in different timezone than you expect). Re the date format change, there are plenty of posts around that already in the community if you search.
The times aren’t “off”, they’re just in a timezone other than the one you want. Velocity {{my.tokens}} can switch timezones for you, search past posts on the topic.