With the functionits capabilites, I am able to do tons of things. With its capabilites, I am able to do tons of things.

Maybe what you meant? "function" doesn't fit very well here.

First, I can search for information wthat I want to know. First, I can search for information that I want to know.

It is very helpful when I want to find a restaurant during travelings abroad. It is very helpful when I want to find a restaurant during travels abroad.

"during" seems to be quite a difficult word to use. I can't explain why your sentence sounded odd, but it did - easier to use "during" with normal nouns than with gerunds.

Next, I can see many videos whenever I want to see. Next, I can see many videos whenever I want.

No need for repetition here.

So there is no need to wait for the time when broadcasting the contenthe content is broadcast on TV. So there is no need to wait for the time when the content is broadcast on TV.

I am able to see old videos which are hard to seefind. I am able to see old videos which are hard to find.

"hard to see" is more like it's a very small video, or something :) you need a telescope to see it!

With the old videos, I can remindember my good old days. With the old videos, I can remember my good old days.

Or "I can be reminded of my good old days"

What else,? I can listen to music with many live streaming services. What else? I can listen to music with many live streaming services.

Plus, I can store my photos and documents on cloud services safely and conveniently. Plus, I can store my photos and documents on cloud services safely and conveniently.

So, Tthese are the reasons why I like the internet. So, these are the reasons why I like the internet.