How does one...gain weight?

Kinda a weird question because most people here are asking how to lose weight.

I'm currently 115 pounds, but I'm 5'9 tall, almost 5'10. I eat shitloads of food every day but I never actually gain any weight for some reason.
My mother's side has a history of hyperthyroid; I think I have hyperthyroid too, but just luckily not as severe (my mother was much worse than me).
I'm Asian, thus my diet mostly consists of rice. I would say my average diet includes half rice, one quarter vegetable and one quarter meat.

Breakfast diet:
Not much, just either a small bowl of congee or some donuts or bread or frozen waffles or something like that.
Lunch diet:
Big bowl of rice (imagine udon bowl size)
Toppings covering bowl of rice, basically just meat and vegetables.
Dinner diet:
Basically 1.5x of lunch.
Later snack/midnight snack:
Half of lunch

So, what are my options for gaining weight? I've heard these so far:

1. Eat different starches like potato and wheat (bread and pasta and mashed potatoes). I heard that these types of starches are better for gaining weight, but I'm not exactly sure how effective it is at making me gain weight.
2. Eating five-ish meals per day. Basically breakfast, lunch, dinner, after-dinner snack (usually just another bowl of rice and some food), and a snack just before I go to sleep (usually a small bowl of leftovers or some dessert and stuff). Not sure how effective this is either...
3. Eating more sweets? Not a huge fan of sweets so I don't eat cake and stuff alot, I prefer salty foods. How effective are sweet foods at gaining weight?

At the same time, what are some good options for working out?
I'm decent at running, I have lots of stamina if I jog at a decent speed but shit stamina when exercising vigorously (I'm known as the five-minute man whenever I play badminton lmao)
My arm strength is shit, where should I start there? Lifting weights?
Core strength is alright, I guess, I should do more pushups and shit though.
I'm pretty flexible overall, too, I guess (lmao)

Okay let's establish this first before we get anywhere. You do not eat enough. Before you try to start getting big weight gain, you need to go get checked to see if you have the issue of hyperthyroidism. If you do, I don't know why you're eating salty foods (Unless you're using it as an excuse for high metabolism). Assuming you don't actually have an issue we'll get to weight gaining.

You need to count your calories, clear and simple. Many beginners will ALWAYS overestimate, I did this myself when I was in high school. You simply do not eat as much as you think you do. You need to find out what your total daily energy expenditure is (Use an IIFYM or TDEE calculator, simple google search) and find out what your maintenance calorie intake is. You want to eat above that, by how much depends entirely on whether you'll be working out as well, how structured and disciplined you will be with your diet. Use an app like myfitnesspal for convenience and log EVERYTHING you eat. Buy food scales and measure out portions if you have to.

At your weight and height, you need to just eat whatever you can and whatever your appetite can fit in. 115 is quite underweight but you shouldn't immediately start eating yourself sick. Measure out your portions, make a meal plan and gradually increase your calorie intake. Drink things like milk to help expand your appetite, don't drink water during meals (takes up space in the stomach) but afterwards instead. Eat calorically dense foods like peanut butter and there's a million other things you can do.

The logic behind eating more meals is you have smaller portions, but you eat more often. So rather than 3 big meals a day, you have 6-8 meals that are maybe 1/2 the size of a regular meal. Eventually your body will adapt and require food every 2-3 hours (or however you want to structure your meals). This is a common strategy for many people to use. Use something like "eatthismuch" to plan out your meals.

Eating sweets gives your body an insulin spike that helps with the carb intake and for a little bit of energy. Have some sweets after a meal, fruit is good.

Options for working out depend entirely on your goal. If you're looking to get "big" then any hypertrophy based routine will work fine as long as you keep eating and keep working out to prevent getting fat.

You need to hold yourself accountable and not bullshit yourself with excuses though. If you're gonna be serious about it, you need to commit to it.

My brother is the same. He's 17 years old, 120 pounds, 5'8-5'9.

He eats like a pig, and still can't gain weight. He also consumes a shit load of sugars.
If your genetics are like that, I think there's little to nothing you could do.

On the bright side, better be skinny than overweight

you need more protein in all your meals
breakfast I would add peanut butter and an all natural protein shake with it

through out the day have healthy snacks like a granola bar, fruits

will will want to be eating 6 meals a day

Salty foods can be bad for your hyperthyroidism.

Let me put this in it's simplest form possible so you can try understand. A calorie, regardless of what macronutrients are in it, is still a calorie. If you eat more calories than your maintenance requirement, you will gain weight, regardless of what you're eating. If you eat below your maintenance, you will lose weight. This is human physiology at work. It is simply how the body works.

Yes eating donuts can help you gain weight, it'll be shit, fatty weight, but weight nonetheless. I obviously do not recommend this. When people say sugars, they don't mean sugary foods but are rather referring to the effects of sugar on the body. We need sugar to function. It gives us an insulin spike for energy and usually a quick burst of it too. You want to try and stick to healthy or low G.I sugars that provide a slow release to continuously give you energy and to help with nutrient absorption. Eat fruits or if you want, any sugary junk food with your regular meals to: 1. Pack on extra calories and 2. help kickstart your digestive system into absorbing the food.

Trust me, looking at your current diet, it honestly does not look like that much. If you want to PM me a picture then go for it but unless you've been doing calorie counting or macro tracking for a long time, almost 99% of beginners always overestimate their calorie intake. I've done it, my mates have done it, people who work with me have done it as beginners. Accuracy is something you'll eventually get the hang of, but for now, you really need to start tracking.

As for foods, food like eggs (yolk included), avocado (probably too expensive as you're in high school), more beef, cooking everything in olive oil and potatoes will help add on calories. Also having high calorie protein shakes (don't buy overpriced mass gainers, just make your own) will easily help put down 500+ calories.

Ignore people saying genetics blah blah blah. Even if you were a "hardgainer", once you commit and start tracking and eating more than your TDEE, you will 100% see results (Assuming you're working out). Don't listen to the broscience of "cardio kills gains" either. Whilst I wouldn't say do a lot of cardio, you should maintain a decent level to ensure continued cardiovascular health.

eat junk food and don't stop.

this is my problem too. I quite eat a lot, but still i haven't gain that much.

Eat more calories then normal, your body will adjust. But be careful, don't eat snacks to get calories.

I want to lose wait not gain

Just learn how to count your daily calories if your weight is standing still just add more food to your daily diet until your weight starts to grow. But do not need to dramatically increase the number of calories, do it gradually. And do not eat fast carbohydrates (sweet, flour) eat "slow carbs" such as rice. Share your meals 4-5-6 meals, no need to eat a lot at a time. You can also try to use a gainer, it helps in a lack of calories, for example when you are at work and can not fully dine