Are there any regulations, either in US or Europe, regarding minimum dimensions for airplane seats, i.e. leg space, horizontal distance, etc.? I ask this also in relation to some (often low cost) companies that often sell extra leg space or things like that; so besides knowing the airplane model, are there still some 'personalizations' the carrier can ask for?
I can't figure out if you are mainly asking about regulations or about possible differences between planes from the same model that might interest a traveller. If you want more details on the former, you might consider asking on the aviation sister site but regarding the latter, there are definitely differences.
Airlines can and do ask plane makers like Airbus or Boeing for customizations in interior design. Differences includes class configuration (how many first class and business seats), the amenities and the seats themselves (there are big differences especially in the premium classes), the size of the seats and the distance between the rows. Insiders call this the “hard product”. As pointed out in the comments, it's even possible to change the interior configuration on an existing plane after delivery (although immobilizing a plane for that costs a lot of money).
Case in point, the number of seats on an Airbus A320 (a common choice for short-haul low-cost flights) can be between 150 (in a two-class cabin) and 180 (in a ‘high-density’ single class configuration). Similarly, the Airbus A380 is certified for up to 853 passengers but nobody has ordered one with so many seats and each operator uses a different configuration, sometimes even two.
Beyond that, some rows have to be further apart for operational reasons (emergency exit rows, row at the front with the passage to the front door or a bulkhead in front of them). Traditionally, you could get a seat there by chance or, possibly, by being clever and asking for it while still paying the same price. But some airlines realized they could scrap a little bit of profit by selling those seats at a small premium. That's the origin of, e.g., Easyjet's “XL” extra legroom seats (they did not order new planes with specially designed “premium” seats, let alone a a kind of two-class cabin, they just happened to have 12-18 seats with more legroom on each plane already). One drawback is that you can't put anything under the seat in front of you on these rows.
There is a website called seatguru with a huge wealth of information on seat dimensions and cabin configuration on various airlines. Glancing at their short-haul economy comparison chart, you will see that seat pitch (distance between rows) ranges between 28 and 39 inches (almost 40% more!) across all planes and airlines. Similarly, seat width is between 16 or 17 and 20 inches.
Bottom line: You can't assume that flying a given plane model guarantees you will have the same leg space.