Hello, I would like to help you.
1. El domingo, cuando ya estábamos llegando a casa se (nos)estropeó el coche.
You can omit nos but, in Spanish language we usually use (nos) because is our car. If you omit nos, you will refer to anyone. These words are called: pronombres posesivos. These words are used when we need to specify who is the owner of the things. For example:
El domingo, cuando ya estábamos llegando a casa se le rompió le coche.
If we write le, the car is not our car, it will be the car of the third person (he's or she's car).
However you can omit nos and write: El domingo, cuando ya estábamos llegando a casa se rompió el coche.
Maybe, the other person who is talking with you could ask you who is the owner of the car.
2. El día de Navidad hizo un tiempo estupendo y por eso nos fuimos a la sierra a ver la nieve.
In this phrase you can't use se hizo o hicieron. Hizo: this word is the third person of the simple past (modo indicativo - pretérito perfecto simple). I don't know if you are studying the verbs and the tenses.
El día de Navidad hizo = él hizo. In this sentence- El día de Navidad... is consider as Èl o Ella.
I hope I have been able to help you with your question.
Regards,
Gloria.