I don't get the questions about food. The whole point here, and ultimate goal, is parenting the child, right? So you parent. Learn to think like a parent. (how old is the child? diapers?) Everytime you go, have your regular kid bag. Healthy snacks, a meal, kids own bottle of water. If needed, diapers, diaper rash cream. No one should be telling you what to supply because you are dad, you need to do all these things. Bring a book to read to child if/when she gets tired. Walk her around and hold her if she's tired, maybe she will nap. (all parenting advice, not legal advice, however your GOOD parenting skills should be noted at the visitation center and will help you)
Why did you address whether or not you should be bringing meals to daughter? That takes so much credibility from you. Start acting like a parent.
The other stuff, as bluntly pointed out to you, could backfire on the mom IF you aren't acting like a jerk about it. Keep a mantra going...when there is drama, I will NOT be part of it, I will not complain around those part of this, I will not engage in the drama, I will not cop an attitude, etc. Find a good friend you can stay in touch with to do all your complaining. If you can keep that part, everything is actually going fine. Your progressing with your supervised visits, unless you screw up they will go away, you got increased visitation time, etc.
When you document, briefly write out what happens when mom late. Document as well your time with your daughter. Briefly; what are her behaviors? How long does it take to bond? Simple stuff. No matter if the supervised facility documenting, YOU keep your journal for each and every appt there.
When is your next court date?