They pay income tax, as does every citizen with an income above a certain level.
The 501c(3) Religious tax exemption deals with the Church Corporation assets, not any of it's paid staff.
That's not to say that the Osteens don't have a bunch of accountants arranging for them to write off a large part of their income, but Mega-Church ministers are hardly unique in that behaviour.
The jet-in church’s name.
The cars- in church’s name.
Not if they structure things right. The salary would be taxable at normal rates, but not the housing allowance, the car allowance, the library allowance. I'm not sure how the cell phone allowance is treated.
For many pastors, half to 2/3 of the compensation is not taxable as income. And they can opt out of Social Security taxes.