I don't know about the eyebrow tension you mentioned. Everything else you mentioned sounds like it's due to a lack of uninterrupted sleep and maybe a lack of properly cooked food too. To answer your questions:
1. Yes, your eyes will heal extremely slowly whenever you get any amount of sleep or a nap. But healing is most effective and long lasting when it's 7 or 8 hours of uninterrupted sleep. At least in my case, the waking up in-between, was the result of eating foods that were not cooked properly, and due to a lack of certain types of food sources (hence the need for a balanced diet). Hope you noticed the "stomach test" link.
2. There's no fixed number. You are supposed to close your eyes for as long as it takes for the strain to subside. In my case it's approximately 5 minutes.
3. Again, there's no point measuring the amount of protein consumed per day. It depends on how much physical activity you do. Similar to how my body tells me exactly how much water I need when thirsty, I eat as much meat as I need to satiate the need for meat. If you are talking in terms of supplements, that's something I've never tried, since the body absorbs nutrition from natural sources much better.
4. My strain was chronic. I'll have to check my notes to be sure, but from what I can recall offhand, the pain from the eyes simply being open didn't last for more than perhaps a few weeks, since I had started taking sick leaves and started ensuring I didn't strain my eyes too much, at that time itself. However, the constant soreness all over and around the eyes, lasted around 6 years or more.
5. Yes, I was working while trying to get rid of the strain. Since I was at work, I had to use the computer at least 6 hours a day, but as I've already mentioned, it's better not to exceed 4 hours. To be an author you don't need to open your eyes that much. You can learn to 'touch type'. There are also various software that can read aloud what you've typed. There are even blind people who do computer programming. An internet search will show you. It's hard to give you a timeline, without knowing the severity of your strain and how good/bad your sleep and nutrition is. These are things that researchers should have worked on, to give us specific numbers and a way to measure the strain. Sadly, their research is going in the wrong direction. Which is why I wrote a guide for them https://nav9.medium.com/a-guide-for-people-researching-eye-strain-6d12c47c7167.
6. Eye pain can mean a lot of things (a search for 'what are the causes of ocular pain' will show you). That should be evaluated by a doctor. What you could do, is to create a scale of pain like this https://en.wikipedia.org/wiki/Pain_scale, but specific to your symptoms. It'll help give you a method of measuring the pain. It'll also be necessary to specify which part of the eye is paining. It's hard for me to say what's happening in your case, since I don't know if it is entirely caused by fatigue and sleep loss or whether there may be some other underlying condition.
I've had chats with people from north and south America and have noticed a pattern of unexplained digestive issues resulting in sleep loss and hence eye strain. Recently there have been people in India also complaining about it. Whether it's due to pesticides or microplastics or the excess hormones or antibiotics given to farm animals or whether it's due to certain medication taken by people or the wrong power spectacles, it has been very hard to figure out. My digestive issues subsided only after I started cooking on my own, and avoided all sorts of packaged products and bakery items. Almonds have given me deeper sleep. Milk, curd and chicken have helped with longer duration sleep. But recently something seems to be seriously wrong with the quality of milk, curd and chicken, so I'm struggling to find reliable sources of food. For you, I'd suggest that you ensure a balanced diet, cook your food well, and maintain a detailed journal of what you ate and what symptoms it caused. In time, it'll reveal patterns of what could be causing the issues. That's how I figured out how to heal myself. It is disheartening that doctors are quite clueless about what to do, but it's also necessary to consult them, since they can identify patterns from their experience. Do try your best to get better sleep.
