I have PDA too and can relate so hard. Every time your parents ask, they're adding to the problem. It can be really frustrating to get around, and on top of that there's the hypocrisy as well. That actually sounds horrible I'm really sorry you're going through that with your family.
Your reply where you mentioned being homeschooled clicked a lot of things in place, it means you'd be eating mostly at home. Where all the comments happen that prevent you from eating. Oh man... no wonder you're getting that sick feeling if food is surrounded by so much anxiety.
Like, leaving your room to get some popcorn is no big deal. But your mum had to demand you three times in a row- and on top of that, treated your PDA like it's some attitude thing. Yeah I can see why you had to rant a bit. Now I'm ranting too lol.
It can be annoying when people can't seem to change a few tiny things in their lives that would be of no difference to them, but would allow you to eat, shower, or do anything else. This is just in my opinion, don't need to take it, to me it looks like if they stopped commenting on your food, that would probably solve a lot of the problem. It is hard to eat with PDA alone, but I will just lay it out all out here...
In your first post, you said you don't eat often and don't eat healthy. Let's review the comments of your parents: your dad saying "you need to cut down on junk food". Well now you are going to avoid cutting down on junk food. Your mum saying "you need to eat something healthy". Now you are going to avoid eating, and avoid eating something healthy too. I know these are just one-off examples you gave, but that's the gist of it. On top of that, if you make a demand of yourself to eat food (by accident), you will have to avoid eating food. So, you're going about your whole day trying to not think of food so you can eat. However, you're homeschooled. Before you have a chance to calm down and think clearly from the previous comment, there is yet another comment about food. Is this right or am I absolutely off track? You don't have to answer by the way it's chill
I had a similar issue with cleaning my room, so I got myself a roomba. After that, my parents saw my room was clean enough and lost interest. Wish I could give you more advice on what to do, but you'd know your family best. I imagine anything that stops those comments might make things a bit easier. Like education, a new location, earphones, maybe something else to nag about instead...