Is supplicating to prophets and righteous people and invoking them considered polytheism (shirk), and are the prayers and fasting of one who does so accepted, even though their supplications may sometimes be answered?

Supplicating to other than Allah is major Shirk (polytheism). Verses from the Holy Qur'an and Hadiths confirm that Du'a' (supplication) and Nadhr (vows) are acts of worship that must be directed to Allah Alone. If a request is fulfilled when supplicating to other than Allah, it is a trial and a test from Allah, not because that other entity answered the supplication. Allah Alone is the One Who benefits and harms. Those who supplicate to other than Allah must be advised, by explaining the gravity of their action and the necessity of repentance.