1- Is it wajib to pray namaz of entering a mosque after entering any new mosque?
2- My father's house is far from mine so do I need to pray Qasr namaz as it's too far and same case with uncles

by

1- No. It is not wajib, but it is highly recommended.
2- If you are living in the same city, then, the answer is NO.
If they are living in other cities, that are 22 kms or more faraway from your city's boarder, then yes.