Shall I go and see my advisor's father who is on his death bed?
Unless you have some direct relationship with his father, this is not something we'd normally do in US, UK, or Australian culture. (I'm not sure if it's the same everywhere in the EU.)

A polite option might be to tell your advisor something like "I'm very sorry to hear about your father, please let me know if there is anything I can do."

If your advisor is from a different culture, that might change things.