This weekend, I can’t make any plans that my willI want to do because I am attending field training, and ithe training will last untilthrough the weekend.

You didn't need "the training" again in the second part because you just mentioned it, so the reader knew what you were talking about. It's not wrong to put it there, it's just no very common unless you're trying to emphasize something.

"I am" is commonly written as "I'm".

I have been thinking of havtaking a free weekend off so that I can drive my mom to my home village, because she has been waiting to go home having a looksee it recently.

"I have" is commonly written as "I've".

In addition, my niece has been going to her first work placejob for more than one month, and I have been wanting to visit her because her work placenew job is 600 kilometers away from my hometown.

"I have" is commonly written as "I've".

These two goalsI have non't been finished until nowable to accomplish these two goals yet.

I don’t know when I can finishwill be able to do them.

While this sentence is grammatically correct, it doesn't make sense because going on a trip to see someone isn't something that you really "finish". You finish a project or a period of your life, (ex. university), but you go and return from a trip.

This weekend, I can’t make any plans at my wills I wish, because I am attending field training and the training will last until the weekend.

I have been thinking of having a free weekend so that I can drive my mom to my home village because recently she has been wainting to go home to havinge a look recently.

In addition, my niece has been going to her first work placejob for more than onea month and I have been wanting to visit her because her work place is 600 kilometers away from my hometown.

These two goals have not been finished until nowyet.