It depends how you define oil and gas subsidies. The disingenuous would add in tax deductions offered to any business and call it a subsidy or assign an arbitrary dollar amount to CO2 emissions.
Other than a few state level incentives, there are no oil and gas subsidies.
Energy is a capital-intensive industry. So you end up with a lot of write-offs for depreciation. But you are right -- these are not particular to the energy sector, and other capital-intensive industries (e.g., airlines and shipping companies, railroads, some types of heavy manufacturing and construction firms) use them just as much.
There is kind of a point that the uncollected social cost of carbon dioxide emissions constitutes a "subsidy" of sorts. It is a cost burden "they" (back to that in a second) impose on society, and society not making them pay for that maybe would constitute a "subsidy" in at least economic terms. I would argue, though, that the ones would should pay that cost are end-use consumers, not the energy industry. After all, nobody ever pointed a gun at me and forced me to drive a car with an ICE engine, to use a gas furnace, or to hook up my TV to a coal power plant. Consumers are the ones who want the low cost and the high levels of convenience and reliability associated with fossil fuels, so they should pay.
Of course, that is not how they use the term "subsidy." They mean it as if we write big checks to the fossil fuel sector for no particular reason, so why shouldn't we write big checks to clean energy sources?
(1.) We don't. Not in the way they mean it.
(2.) We already do. We have had a wind PTC since 1992 just to provide one example.