Images on Facebook page appear too small.

First of all, choose a plugin and stick with it. You had three plugins managing OG tags, and you manually added OG tags following the article you linked to.

You only need one method, having more than one will cause conflicts.

I use WordPress SEO for this, it does a decent job and provides a default image for when Facebook finds none.

Second, Facebook will choose whatever image it finds to be suitable on the entire page. There is really no way to control it beyond providing a default image for when it finds none.

You can check info on a specific link via https://developers.facebook.com/tools/debug/og/object/ (and use the “Fetch new scrape information” button). Right now, for the link you provided, Facebook is fetching the image within the article.

I tried different plugins as one wasn’t doing what I wanted it to do, so I kept trying with another.
But I get it that it may cause conflicts

I dunno of this is a Facebook issue or I have some wrong settings in WordPress. But my issue now is this:
When I paste this link https://cuckoopress.com/2015/01/08/minister-di-hustisia-ku-plan-pa-arma-komersiantenan-den-zona-di-peliger/
on the Facebook debugger page, it fetches the right image, and on the preview, it comes on just fine. I chose a big 400×282 px image so I want Facebook to display it big too. It attracts more people like that.

I also tried pasting the link directly on my page, and it shows just fine prior hitting on the post button. But as soon as I hit the “post” button, the image(thumbnail) becomes a teeny tiny thing. I don’t want it like that.

On my Facebook profile, and on groups etc…..it shows just fine.
Why doesn’t it show fine on my Facebook page as well?

Ah, that’s a Facebook thing. Facebook controls how everything is displayed, and lately it seems like Facebook Pages have been getting the short end of the stick.