1) Should I recite his name or his mantra?
Greetings to you.
1. You should continue to recite his name, but more frequently every day. It’s not advisable to recite his mantra because it will require much from you, including that you become vegetarian, abstain onion and garlic, and more.
2. You should go and seek advice from those monks in Vietnam who practice the Medicine Master Buddha Dharma. I am not sure how they go about it. Nevertheless, I advise to start with bowing to Medicine Master Buddha every day for half an hour to an hour. You can also place the Medicine Master Sutra on the altar and make offerings to it frequently. That is how I would get started: by bowing and making offerings.
3. It would appear that your father and younger sibling are possessed by yin beings, as you suspect. This is not good because the rest of your family is also exposed to possible problems. Perhaps you should ask those monks you mentioned above for help? If you were here in the US, there are competent temples that can really help that I would be able to recommend. Unfortunately, I don’t know of a temple in Vietnam to suggest. There should be, but I am not aware of any. Perhaps, if you bow, make offerings to the Sutra, and recite his name more sincerely, he’ll point you to the right one.
My best wishes!