Whenever a definite noun is used together with an adjective, an article is placed in front of the adjective. So should not it be, "Hon studerar nästan den hela sommaren" ?
hela is a special case, I don't know why but it doesn't take the article. Great question, though.
why hela instead of helt
You need the definite form, which is hela.
I don't wanna be that guy but why do you need the definite form?
Because you say "sommaren", the definite form.
Why is not sommar instead of sommaren ?
Literal translation: "She studies nearly all the summer" This would not be an entirely unusual construction in English. I suppose it implies a specific summer in which she is studying.
Compare with "nästan hela dagen" and "nästan hela veckan"
You would need to say 'studied' all the summer to make it a definite summer. 'studies' is with the indefinite form which speaks about summers in general
Why it is not correct when I translate it into she studies almost all the summer
It's either "all summer" or "all of the summer".
Shouldn't läser be accepted? Doesn't it also mean study?
"Läser" can totally be used for "study" in the right context. E.g. "Hon ska läsa nationalekonomi i höst". = "She's going to study economics in the autumn."
But if you say "hon läser nästan hela sommaren", it very strongly sounds like you're saying she reads all summer.