This week I gi*gave* myself a task.

You already gave yourself a task, so you should use the past tense.

Each day jogging*I will jog for* one hour and practice 2 hours snooker*snooker for* 2 hours.

I would say I completed half the task.

Did you complete half of one task? That's what it says now. Or did you complete half of all the tasks? If so, you must say "tasks".

The second day was hard, I so *wanted* to give up.

By using "wanted" (past tense) we understand this was something in the past. Right now, you are saying you still want to give up.

But now (the 3rd day) I think I can complete the task.

Do you mean one task or both tasks? If both, then you must use the plural word "tasks".

Now I got*have* the confidence to attempt another new task.

In fact, I already set up a new challenge to me*for myself*.

When you *are* physically strong your mind *is* strong too!

Some verbs were missing.

Complete 3/7

Nothing wrong with this title!
It attracts the reader simply because it is not clear what it means or what is going to follow in the text! This is unusual for titles because they are supposed to identify what you are going to speak about. But I think it works well here.

This week I giave myself a task.

Each day jogging one hour and practice 2 hours snooker.

The sentence needs to be more closely associated with the previous one above. Suggestion:
This week I gave myself a task: each day jogging for one hour and practising snooker for two hours.

The second day was hard,. I so much wanted to give up.

Now I gothave the confidence to attempt another new task.

In fact, I have already set up a new challenge to mefor myself.

When you are physically strong, your mind is strong too!