Is it possible to disable image editor or change some function of it?

I prepare images before uploading so neither is bigger than 800px and 100 kb. When I upload it as the item image, it ends as few images and some of these are more than 200 kb each.

I would like to have only original photo (which is less than 100 mb) or maybe this one and one or two small (eg. medium and small)

You can use an extrafield instead of K2's image.
There are a lot of topics in the forum which offer a complete guide.

Too complicated plus some of my categories already have extra field group associated. I would like to disable image editing. If that's not possible, I'll just choose to show the first photo in modules and categories

This can be done with a plugin like: getk2.org/extend/extensions/616-iaki-import-as-k2-image

This sound perfect for what I need - fetch the first image from the article body and assign it to the image positions used by K2 in all the K2 views (probably even as og:img, I hope) - but it's not working for me. Have any idea why?

It won't work with OG images, you will have to manually develop a script for this.

As for the plugin, are you getting any errors, is the plugin enabled?

.

plugin is enabled, no errors (only the notice about a future version of PHP) but nothing happens
see it here: www.get4u.hr/hr/putovanja (at the first page all items but one have k2 image)

Are you hiding K2's image in the category's settings?

No. This link is for category blog.
In the meantime, I figured out this: it works only with new items but in a strange way - it assigns some random old photo from k2 cache folder and not from the content. With old items, it doesn't work at all.