Peter also promised a reward in heaven to leaders who ruled well. What did he promise?

Peter promised leaders who ruled well would receive a Crown of Glory.

Source: 1^st Peter 5:4

While Paul did not take money himself, he did say it was right to pay leaders. He quoted “Thou shalt not muzzle the ox who treadeth out the corn”. Who was he quoting?

Paul was quoting Moses. He quoted this to the Corinthians and to Timothy.

Source: Deuteronomy 25:4, Quoted 1^st Corinthians 9:9 1^st Timothy 5:18

Paul as a missionary and preacher could have asked for support. But he made his own money working at this trade. What did he do?

Paul worked as a tent maker to support himself. Even today self supporting ministers are sometimes referred to as tent-makers.

Source: Acts 18:2-3 Acts 20:34

To provide for the priests and their families God permitted them a portion of most offerings. Which offering could they not consume?

The only offering the priests could not consume was the burnt offering.

Source: Leviticus 1

What part of the promised Land did the tribe of Levi inherit?

God commanded through Moses that they were to have no part of the land or inheritance.

Source: Deuteronomy 10:8 Mentioned in other verses also