이해 했어요
It means I understand/understood it?
Is there different tenses in Korean?
이해 means understand.
Where is "I "?
I refered to the dictionary,I is 가
But there is no 가 in this sentence. Why?
There is always a 요 at the end of the sentences, does it meaning nothing?just a "tone\mood word"?
고맙 습니다

Question

Answer

이해 is a noun meaning understanding   
이해하다 is a verb meaning understand

I guess you know 이해 is from Sino-Chinese 理解.
Unlike Chinese, a noun word can be a verb by adding 하다 in Korean.

이해하다 -> 이해했다      added past tense suffix (았,었)
         -> 이해했어요    added honorific suffix (요)
         
In a conversation in Korean, subject "I" is mostly omitted.