I spent my morning there studying.

it sounds more native to say "my morning" in this context, or alternatively "the morning"

I wanted to have a Gimbap for lunch.

when we talk about dishes, we don't to specify a number or use "a", example; "I wanted to have pizza/ sushi/ fried chicken"
or you can put "some"

But the diner that I wanted to go to was closed.

Two of the diners near the library wasere closed.

I gave up my lunch.

when you say "gave up my lunch" it sounds like you had it in your hands then gave it up for something or someone, as in you used to have it but no longer do. In this context what you can say is "i gave up on having lunch"

There wasere two hours left before my girl friend come.

Tiny buds clung on every tree branches.

I can feel my heart thumping after sprints.

The one was fried and the other was with broth.

But It was a shame that foods are disapointing.

see explanation below for food

We couldn't eat much of them.

it's more coherent to just say

I've been looking forward to it but the foods fell short of my expectation.

food can't be made into plural, it already implies a quantity of some sort

To me, eating out is getting more disapointing.

truer words were never spoken

And I spend more time ton cooking.