What are the situations in which it is permissible to shorten and combine prayers when returning to one's parents' hometown (a distance of more than 100 km) for a few days, bearing in mind that the current residence is rented and the parents' hometown has an owned house?

If you have not made the country you work in your homeland, and you are still a resident of your original country, then you should not shorten or combine prayers when you come to your original country, because you are still a resident there. As for shortening prayers in your country of work, it is conditional upon residing there for the duration of the shortening (4 days or less), and upon there being a travel distance between the two countries exceeding 83 km.

And if you have made your country of work your homeland, then it is not permissible for you to shorten or combine prayers in your original country where your family lives and where you own a house. Rather, it is sunnah for you to shorten prayers and permissible to combine them while traveling between the two countries if the distance allows for shortening. Some scholars are of the opinion that it is permissible to shorten and combine prayers in your original country because it is no longer your homeland.

It is advisable to avoid disagreement and refrain from combining prayers, to maintain congregational prayer, and to pray the full prayer if you are led in prayer by a resident.