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" ?
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
"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.