1) In an article, I read this

The number of international terrorist attacks increased by 8 percent last year.

The number of international terrorist attacks increased by 8 percent in the last year.

The number of international terrorist attacks increased by 8 percent over the last year.

This is semantics. All of these mean the same thing.

2) In another article, I read this:
"More than 6 million people visited Iran in the year ending March 2017, up 50% from the previous year."

Using "on" here is silly. It is the writer's style. The correct word to use is "from."

Sometimes I read "up/down % from last year" "a increase over"

And why "on the previous year" and not just "on previous year"?

Because you need an article. I don't know why.

To use a sentence without an article, you would say:

Sales are up 8% from last year.

Hope this helps!