Is it possible to customize already existing theme so that it is more wide horizontally and gets rid of unnecessary space vertically so that the comments and posts are as compact as possible like in this website? Likes, reply, etc. should be relocated to the same line with username but in the right corner?
You can change almost anything visually using CSS. We’re not going to be able to provide you with the specific CSS, as there are a lot of changes needed. You can check out my post on using the built-in Chrome developer tools, and play around with finding what you want. Alternately, you can try posting in the #marketplace if you have funds to pay for this.
Changing width and relocating buttons?
Discourse is responsive, and width and button positioning adjust with the width of the browser. You have to be careful not to break that, or you’ll be forcing your users to scroll left and right while reading.
Edit: I feel like this has come up before, I’d suggest searching through #support - you may find something useful.