In fact, I don't need to learn English, but I have a lot of spare time and I just don't want to waste it.

Better: Actually, I don't need to learn English (for my job/school/etc.), but I happen to have a lot of spare time and I want to make good use it.

In fact, speaking English is not a big thing,deal; it is just a basic skill.

Better: In fact, being able to speak English is no longer considered a big deal; it's just a basic skill.

Nowadays, even children, elementary and middle school students, can speak English well.

Are we not as good as children?

This is grammatically correct, but who is "we" here? Adults? People of a certain generation?
Here's a suggestion that I think captures what you're trying to say: "Are people of my generation losing out to middle-schoolers now?"

We have a lot of fragmentary timeee time throughout the day and we can take its advantage of it to do many meaningful things.

Once again, the "we" here is ambiguous.

If you are able to mMastering English, it can givebring you a lot of benefits.

For example, no matter which country you go to, you will not haveencounter a language barrier because English is an international language.

So, even though I am atof such an old age, I still decided to learn English well.

"I am of such an old age" is a bit wordy. I would say, "I am old" or "I am advanced in my years."

"I still decided to learn English well" sounds a little bit off to me, though I believe it's correct. You could say, "I still decided I want to learn English well."

Although I can't speak English fluently at present, I believe one day I canwill make it to this goal and theat day will be coming soon.

In fact, I actually don't need to learn English, but I have a lot of spare time and I just don't want to waste it.

Starting you discussion of learning English with "in fact" sounds a little strange. That's usually used to present additional information, as you did with your next sentence.

In fact, speaking English is not a big thingdeal, it is just a basic skill.

Nowadays, even small children, elementary and middle school students can speak English well.

Elementary and middle school students are still children, so it makes more sense to specify very young children.

We have a lot of fragmentaryee time and we can take its advantage of it to do many meaningful things.

For example, no matter which country you go to, you will not have to struggle with language barriers because English is an international language.

As a native English speaker who's traveled abroad I can tell you this isn't always true.

So, even though I am at such an old age, I still decided to learn English well.

Although I can't speak English fluently at present, I believe onthe day I can make it and the day will bewill be able to is coming soon.