What can I do to help me sustain frequent long-ish rides?
Just keep at it. The human body is very adaptable and you'll soon get fitter.

Don't worry too much about food and nutrition at the moment, that only matters when you're cycling at a competitive level, you just need to make sure you've had breakfast before you ride in the morning. Regardless of cycling/weight loss you should try and eat a healthy balanced diet anyway.

Don't worry about heart rate and zones. At the moment you just need to get to the level where you can comfortably manage 5 days riding. This will come naturally. Its hard at the start (as you are experiencing) but it will get easier every week.

In a month or two you will be able to manage the ride no problems and only then should you think about pushing your performance. That's when the heart monitor is useful.