"I will check this."

Translation: Я проверю это.

[Mutusen]

"Я это проверю" was not accepted, is this order wrong?

[deactivated user]

It's not wrong. According to Rosenthal’s style guide (§ 180.1), both are equally correct. You should report it next time you get this sentence.

[Scian4]

Accepted November 2020

[Ivorah]

Why isn't it я этого проверю

[Kundoo]

That would mean something like "I will check this one", referring to some (male) living being.

[susanashe]

why not ето

[Kundoo]

There's no "ето" in Russian. "Это" is the correct spelling.