If I bought someone's Macbook, can he spy on me? What if someone sold me his Macbook he doesn't need anymore?
When I remove old home profile and reinstall OS via Cmd+R (btw, would I need sudo pass for that?), after that would previous owner be able to block Macbook remotely or get any data about it?
In short:
To be completely sure you would want to go to disk utility when booted with Cmd+R and erase your MacOS partition. 

Some more:
At this point (after erase+reinstall), assuming there were no hardware modifications (in theory you could install hardware tracking modules, wireless microphones and such, but it's rather corporate espionage/P.I./high profile legal domain) you should be good to go.

Booting with Cmd+R and doing just reinstall, without erasing partition can - in theory - leave some parts out.

Remote access is then controlled from system settings and remote wipe can be performed, if you are connected to iCloud (or have some 3rd party app running, which after partition erase you would not have).

The most careless would be to just remove user profiles on newly bought Mac, as there might still be some apps running in background, that you would not even see in Applications folder.