Is there a way (or can I suggest making this possible) to show questions with "my tags" sorted in order of newest to oldest... instead of most votes to least votes?

The reason I ask is that it seems like the top few pages of questions with "my tags" are pretty static (and many of the questions were asked at least a year ago). It takes time to look for something reasonably tractable that has not already been sufficiently answered.

I understand that you're referring to Unanswered/my tags. That page is indeed not very useful, and in fact SE plans to remove "Unanswered" from the site interface.

However, you can use this search link to achieve the same effect that sorting that tab by newest would do. Just bookmark it.

Explanation of the above search query:

intags:mine isanswered:no hasaccepted:no score:0.. closed:no

• intags:mine: has one of your favorite tags
• isanswered:no: has no answer with a positive score
• hasaccepted:no: has no accepted answer
• score:0.. has nonnegative score. You can omit this if you want; I include it because this is the behavior of the Unanswered tab.
• closed:no not closed. Same reason as the previous item.