Tricky tickets.
 

Hello! I am planning to travel to USA from Romania in the foreseeable future and I have a question. I will have some stuff to do in Detroit, Michigan. When I searched for tickets from Bucharest to Detroit, the prices were pretty high, so I've tried searching for tickets from Bucharest to Chicago. I have found less expensive tickets that have a stop in Amsterdam and then in Detroit another stop on the way to Chicago. The way back is the same, that is Chicago-Detroit-Amsterdam-Bucharest.
My question is why these tickets are far less expensive, even though they have 3 flights instead of 2 and both go to Detroit. Furthermore, would I be able to buy the cheap tickets mentioned before and just skip the third flight (the first flight on the way back)?

If you skip any leg of a flight, all legs on that flight after that are voided. On any airline.

So if I skip the third flight on my way to US, the flights back to my country will also be cancelled?

Yes

Supply and demand. There is more traffic between Chicago and Bucharest, with more airlines competing, so prices are lower. Less traffic between Detroit and Bucharest, so prices are higher. The fact that the Bucharest-Chicago trip you're considering involves a plane change in Detroit is immaterial. Airline sell tickets from point A to point B, without regard for the route taken to get there.

Absolutely not. Google "hidden city ticketing" to see what happens. The airlines regard this practice as theft.

Not "without regard for the route taken to get there." There can be enormous differences in prices for nonstop flights versus connections. In addition , certain routings can be more expensive for various reasons, for example on DL, compare SFO-LAX-JFK (D1 service) to SFO-MSP/DTW-JFK (regular FC service).

Tickets between Chicago and Detroit can be very cheap. You might find it is worth it to fly to Chicago and buy an additional ticket back to Detroit.

This is what I'd do.

Except Allegiant :D Too bad they don't fly Bucharest to Detroit. . .