About today

It's sunny in Japan ,today. So I feel so good and relaxed.

It's sunny in Japan today, so I feel good and relaxed.

OR

Today it's sunny in Japan, so I feel good and relaxed.

The day(s) ,like today,make me sleepy.

Days like today make me sleepy.

I have ,however,a lot of what I must study hard.

However, I have a lot of studying to do.

However, I have a lot of hard material to study.

However, I have to try hard to study.

Note- Using "I have, however, ..." does work in English but most people won't say it like that. Keep in mind that you can do it, though moving "however" to the beginning may be more standard. The same applies to "a lot of what I must study hard." Again, this makes sense and is gramatically correct, but it is not a common way to make this statement.

This is because I want to pass the entrance exam of (for) college.
Now I am studying geography.This subject is very difficult for me.

I (will) (have) studied it for three hours.

I will study it for three hours. (future tense) 勉強つもり/勉強します

OR

I have studdied it for three hours. (past tense)　勉強しました

I (will) try hard to study it!

Thank you for reading.

Great job! Commas take a long time for many English natives fully grasp so don't struggle with them too much. It may be difficult in the beginning, but try to use them where a sentence naturally pauses. Keep up the good work and good luck with your studying and entrance exams!