Background is just image added in PS, there is no HDRI only corona Sky, it's really nothing special. And about postpro, I made little color correction, maybe it's too saturated. I'm not so good at it yet (btw Pavel (Romsy) is :).
I have a question, is there any way how to make AO. In Vray, there is a checkbox in Render setting, but i didn't find something like that in Corona. Personally I don't like those very dark (almost black) corners, but for example in render with green chair little bit of AO would help.
Yes, you can get AO, but no, you should not use it.
You are rendering semi-bruteforce GI, so the detail is there. Most of the people use AO wrong. AO is not something that improves contact shadows. It's a legacy method to enhance flat ambient lighting from times, where there was no such thing as global illumination, and then it was adopted to enhance primitive indirect illumination methods as radiosity or final gathering.
But for modern methods, such as properly written irradiance cache, or brute force rendering, there is no reason to use AO.
If you are lacking contact shadows, like in the example of room with green chair, then it means your Albedo (overall material brightness) is too high. Sheet of white paper is usually about RGB 220, very white walls are usually RGB 200-210.... fresh mountain snow is about 230...
People often do a mistake of making materials a lot brighter than they really are. So check your materials for super bright values. Even your wood floor may be a bit brighter than it should be. You can fix that by setting output amount in your bitmap to for example 0.8. That's what usually produces that washed out flat lighting look. I would never go over RGB 230 white.
And high albedo doesn't just make renders look unrealistic, it also slows down the rendering because russian roulette algorithms are having hard time.
So check that... and if it get's a bit darker after fixing material, just compensate for it with exposure.
Lastly... for background planes, environments behind windows and such... use CoronaLightMTL with
disabled emit light option. That's it... it will not cast shadows nor receive any shading, so it's ideal for background plates behind windows.
And try to avoid fakes, like disabling shadow casting and such, because they slow down rendering as well.