I wouldn't say I have a proper training program but I have been a poolee at my function for over a year and I run with recruiters, every once in a while they make us stop and do some form of exercise on the sidewalk (pushups, planks, etc) but we dont keep track of our runtime or distance, we do that only once a month. and How should I go about asking my doctor if I'm good to run? because I took a Pulmonary Function test before and they've checked my lungs and said they were fine about a year ago.
Get another check up and describe the pain you're getting to them, they should be able to tell if you're clear or not. If you're military or training to be military, definitely incorporate interval training. It'll help condition you for the start, stop, start, stop tempo. Hill sprints will also be very beneficial. You could also run with a pack but keep in mind it does put a lot of strain on your knees and may give you long term knee damage over an extended period of time. (Dependent on how often and how much weight you run)
There is an extremely low chance that you have a metabolism outside of the average. Numerous studies have been done in regards to the percieved metabolism in subjects and their actual metabolic physiology. You are simply not eating enough. (This is the case 95% of the time for almost all "hard-gainers"). Take this from me, I used to think I had a fast metabolism but in reality, I wasn't measuring or eating a caloric surplus.
So look up your TDEE (google TDEE calculator) and look up your maintenance requirements. Eat a couple hundred calories about that. Use a calorie tracking app (e.g. myfitnesspal) and see how much you eat in a regular day. From there, slowly begin to add on food. Milk, peanut butter, constant snacks like nuts etc. will help build up your calories. Eat more carbs, make sure you work out. Just use whatever weight you can actually do, if it's the lightest possible weight, so be it. Everyone starts somewhere. I couldn't bench your standard olympic bar when I started.
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Yeah you can, fruits are a healthy way to spike your insulin to help nutrient absorption. Just don't be excessive.