What are the categories of seeking help from Allah and from other than Allah, and when is it permissible or impermissible, with an example, evidence, and ruling for each category?

Seeking aid means asking for help. Seeking help in matters that none but Allah can accomplish is polytheism (shirk) in Lordship. The evidence for this is Allah Almighty's saying: "It is You alone we worship and You alone we ask for help," and the Prophet's (peace be upon him) saying: "If you seek aid, then seek aid from Allah." As for seeking aid from other than Allah in matters that one can accomplish, it is permissible. The evidence for this is the Prophet's (peace be upon him) saying: "Indeed, we do not seek aid from a polytheist," and his saying: "Allah is in the aid of His servant as long as the servant is in the aid of his brother." And the hadith of Sufyan al-Thawri when a man said to the Prophet (peace be upon him): "A man comes to me wanting my wealth." He said: "Remind him of Allah." The man said: "What if he is not reminded?" He said: "Then seek aid against him from those around you among the Muslims." The man said: "What if there is no one around me among the Muslims?" He said: "Then seek aid against him from the ruler."