Factors that make Qurbaani waajib

Performing qurbaani while one is a musaafir

Q: For Eid, I'm going to see my family abroad. I'm only going for one week so I will be a Musaafir. One condition of wujoob for Qurbaani is that a person is a Muqeem. I am planning to do zabah of an animal there. 

The question is what intention do I make? Is it Nafl? If its Nafl, can I then do esaale thawaab of it instead of doing it from my own side? Or will it become waajib when I buy the animal even though I'm a Musaafir?

Obligation of zakaat and qurbaani if one has a share in a property

Q: My father passed away in 2021 and, we, the heirs (mother, and 3 brothers, all adults) inherited property and cash as per shariah.

1.The cash was given by us to our mother. We made her the owner of that cash.

2. The property inherited (2 x 5 marla plots) are combined property of our mother and 3 brothers, the net worth of shares is above the nisaab.

Our mother pays yearly zakat as well as Qurbaani.

The question, Is it compulsory for us 3 brothers to pay zakat and qurbaani, provided that our indiviual monthly incomes/savings are less than the amount of nisaab (cannot even buy or share an animal for sacrifice and neither of us can move/sell, the shares of property, or use for any business means). Will zakat and Qurbani be applicable on this sort of shared property?