How lasted the ship half a year without breaking, etc., how it feeds since it is not a rocket?

Newton's first law of motion, that's how it works. Everything remains at rest or moving in a straight line unless a force acts on it. That is what is happening here.

Therefore, it is NOT necessary to refuel each machine, since once it is moving in a straight line in the direction you want it to go, and it is in space so there is no friction that slows down, all that has what to do is wait and arrive without using more fuel. Cars and planes have friction and the air resistance acts on them because they are not in space, so they DO need their engines to work all the time to keep moving. A better comparison with space is to skate on an ice rink: once you're moving, the hard part is stopping!

In fact, then you need to use your rocket motors to slow down if you want it to land! All spacecraft work like this: you only need a big rocket to start it and get it fast enough to escape the gravity of the Earth. If you keep the rocket firing constantly, the ship will continue to accelerate constantly and you certainly will not want that if it's going to land somewhere. You will need even more fuel to reduce speed again! You will only need small rocket engines to change direction if necessary and yes, eventually they will run out of fuel, so you should plan to use as little as possible.

Which reminds me of Cassini. That went around and around Saturn for years, with a small occasional rocket launch to change direction and see something interesting. Like when the magnetometer found something interesting in Enceladus: should we change direction to see it more closely? That had to be compared with other demands to go somewhere else, given the limited amount of fuel left. Anyway, the team decided it was worth seeing, and discovered a water geyser in Enceladus! Wow, liquid water when it's so cold? Could that mean life? Hmmmm … I bet it will be a target for a future space probe for Saturn.

Exactly the same with Apollo to the Moon. Once it was on the way, no more power was needed until it was time to brake and land.

And with planets and satellites, how do they keep moving with nothing to push them? No friction in space, that's how, so just keep moving.

Now, why do you assume that everything breaks down in 6 months? Certainly not if it is well done. Many spaceships continue for years. Take the Voyagers: they have been going for more than 40 years and they are still sending information. Now they do need electrical power to do that, they have a small nuclear power plant on board, but yes, that will eventually stop working. But they do not need rockets. They continue to advance in the vacuum of space according to Newton's first law.

Actually missions to Mars fail a lot. Landing is the hard part: if you do not do it right, so the thing stops softly, it will crash and that has happened many times. The best of the last thing is that DID went well.

Looking fragile does not matter in space and hitting an asteroid would be surprising, as they are far away. Actually, there are thousands of miles between them and no space probe that crosses the asteroid belt and passes to the planets beyond Mars, has never reached one.