I think the date selector is a must. My biggest timezone confusion happens during these two weeks when the US changes the daylight and the EU is not changed yet. So... during the two weeks in a year 9:00am SF time is not 18:00 EU time.
Yes, same for me! Being able to see not just gmt-5 but also standard vs daylight would be excellent!
We were in an EE/Telco degree where we had to program in different languages and configure plenty of different software, so knowing to solve that kind of problems are relevant in the kind of work they were going to do in the future.
The reality of that is how most of people are (or were?) in those degrees as a mere formality to get a good paying job, and interests are a secondary matter.