Burial for Noahides

[Director Michael]

There may be a problem for the soul of a Righteous Gentile, touch a dead, even if he one of your parents (G'd forbid)?

There is no problem if that happens in a normal fashion and not for any bad intentions.

And if not a parents, but a neighbor, an idolater, but we need to investigate his alleged death, there may be spiritual problems?

There is no reason for such concerns. In fact it is a good deed to care for the process of respectable burial for any human corpse.

Evil spirits (ruchot) does not take possession of these bodies?

Contact with a human corpse transmits spiritual impurity ("ruach ha'tumah") to a Jew, which only restricts him from entering the area of the Holy Temple in Jerusalem. That is a normal thing for all Jews, and it has no relevance to Non-Jews.

It would be wise to avoid such situations? Something like asking someone else to do the "service"?

Only out of respect, a person should avoid touching a human course unless that is definitely needed for some good reason. If it is needed for some good reason, then it is a good deed to do so.

One should try to avoid taking part in a funeral that involves idolatrous prayers, services or rituals. At the most, a Noahide may be a by-stander at an idolatrous funeral service if there will be people involved who will get very angry or insulted if the Noahide person does not attend.