Can I say "in a various way" here instead of "in a variety of ways?" Are these two same thing? What's the difference?

So there's an institute of education for children like Helen Keller?

Globally, many institutes have been established to educate students with disabilities, including learning, visual, auditory, and physical, to name a few. They can be public or private institutions. Additionally, many public schools also have classes dedicated for students with disabilities.

What is "coder"?

A "coder" is someone who writes codes for computer software or programs. Ex: He graduated with a degree in computer science and became a coder.

what does 'just' mean here?

You can think of "just" in this context as meaning "nearly/almost," or "by a very short distance." The speaker has used it here to express that Malaysia is situated very close to the Equator (just North, or above, it). Ex: I live just north of Central Park. Ex: The police station is located just west of the central library.

Why does she suddenly say "dramatic"? Can I use "dramatically" instead?

She says "dramatic" to describe her "dramatic" curled eyelashes. "Dramatically" would not be suitable grammar in this sentence.

Does he mean that he placed something on TV? Or "put" means similar to "turn?"

It's actually not meant in a literal way! To "put" something on TV means to play or watch something on TV, like a movie or show. You can also use this verb with music! Ex: I put my favorite song on and danced to it while I got ready. Ex: My mom always put my favorite TV show on while we ate dinner.