Ok
Yes it is. Many (but not all) words that end in -ly are adverbs. You can use repeatedly to modify a verb. For example, "He denied the accusation repeatedly."
all over the world
No.
it is important to use the metric system because only three countries do not use it and scientist have to comunicate their results all over the world
there is an discrepancy in people all over the world.
Adverb
Yes it is. People all over the world use it.
No, people all over the world use this site.
The sly, brown fox jumped over the lazy dog.
"Use" can function as both a noun and a verb, but it is not an adjective or an adverb. When describing how something is utilized, you might use the adverb "used" in phrases like "used frequently." However, "use" itself does not serve as an adjective or adverb.
No adverb is better than any other; each adverb has its particular use, to convey a specific meaning. Choosing the right word depends upon what you are trying to say. There is no single right word which is always the right one to use in all cases.
Yes, thankfully we can use it as an adverb. It is the adverb form of the adjective thankful.