Assalamu alaikum wa rahmathullahi wa barakathuh

Praise be to allah and peace be upon our beloved prophet and his faithful followers

yes it is prohibited to greet a non Muslim with Salam but you can say hi hello good morning kinda things and if non Muslims greet you with Salam you shouldn’t say wa alaikum salam  instead you should say assalamu ala manithaba’l hudha

and allah knows the best

Praise To be Allah.

Brother has 2 part of the question.

First of all, What if it is Obligatory for My father to go to Hajj or Qurabanii??

The answer depends on Your Father’s ability. If he is able now to give a Qurbani or afford Hajj, It is Obligatory for him.

Hajj is not obligatory except for the one who is able to do it, because Allaah says (interpretation of the meaning): “And Hajj (pilgrimage to Makkah) to the House (Ka‘bah) is a duty that mankind owes to Allaah, those who can afford the expenses (for one’s conveyance, provision and residence)” [Aal ‘Imraan 3:97].

The Second part of the Question is That, Your father is very uninterested about Islam and If you tell him to pray, he tells you that he will give his own answer, It is true. But Do you know What is the meaning of “Marfot“??

Marfot means through. What is the Work of ” through ” in salah. It is you and Allah.

Come to your Question. When you have the ability and your Own Money and all this stuff, you have to do Qurbani and Hajj. But it is not Obligatory for you. But, you have to call them to the Path of Allah with Wisdom and softness. And Do not ever be rude with then. Allah Says In the Quran, 

إِنَّكَ لَا تَهْدِى مَنْ أَحْبَبْتَ وَلَٰكِنَّ ٱللَّهَ يَهْدِى مَن يَشَآءُ ۚ وَهُوَ أَعْلَمُ بِٱلْمُهْتَدِينَ

Indeed, [O Muhammad], you do not guide whom you like, but Allah guides whom He wills. And He is most knowing of the [rightly] guided. Quran 28:56

So, Give them Dawah and do Your best. Inshallah, Allah Will Give you great reward in the Hereafter.

جَزَاكَ اللهُ خَيْرًا