Hi! Congratulations on wanting to better yourself! Here are my opinions on your questions
1. I would start the program and also up my water intake, especially since you are in a desert climate. But always drink water, regardless of if you 'feel' hydrated! Track it if you are unsure.
2. Try to do the intervals but feel free to skip a 'jog' session and walk through it! Do what you feel is correct for your body. And feel free to repeat days!! I stayed on week four for almost three weeks.
3. I enjoy a huge glass of water, yogurt and a banana after my workouts but whatever makes you happy and healthy!
4. I feel like I look like a dork when I jog too. I have short legs and no matter how fast I feel like I'm 'running' (or even sprinting), I'm still taking baby steps.
I hope this helps and have a wonderful day to you!