does updating content pushes ranking up?

Yes it does Always keep on updating your content to rank up.

Substantially changing the main content on a page that has 2000 - 2500 words and is already ranked on the first page is probably NOT going to get you the results you want.

You're already on the first page! They're telling you the content is fine.

It sounds like you might want to focus on building a few quality backlinks.

Yes it does, I've done this when Im ranking on the first page but not on top 1, adding some content can really make the diference. You can also change the date to make it seem ''updated'' it also works but I won't use this method as much.