Answer 2 ) Have your dad to contact US embassy Kathmandu. They will give him a form to fill up and need to pay around NRP 20,000 fee. The form is to reinstate the GC. Your dad has to mention the valid reason ( medical is the best option i think) to stay in Nepal for long time. Either Your dad can come back in USA if they approve it or they will deny it. Then you have file new i-130 for him.
1. No your brother won’t be barred but that doesn’t mean guaranteed entry, it’s up to the CBP officer. Since it takes more than 14 years for your brother to get immigrant visa or GC, i130 petition wouldn’t affect much at this time for visiting.
2. Your father can try applying for returning resident visa at the US embassy with some good reasons. I doubt he will get it since it’s been so many years but who knows. If that fails, then i130 again.
For number # 2: What if he surrender green card and apply for tourist visa saying I don't want to stay there permanently but want visit kids on and off, do they give visa in those case ? Anyone have experience around that ? It's pain to file i-130 and go through all that , if they only plan to few months at a time.
We went thru the same situation. My mom applied for the visitor visa after us embassy took her GC for staying long time in Nepal. They took the passport on the interview day for visa granted and stamp. She got a call next day to come to the embassy and asked about staying long time in Nepal holding a GC. My mom has multiple health conditions including she is the breast cancer surviver which she explained to the consular but they rejected her visitor visa next day. We were shocked. Good luck to your father. My mom's case is in national visa center now after I 130 approved.