Never said the oil, gas, coal industries were the only ones receiving subsidies. Just that they received more than alternative energy which is more in the developmental/infrastructure building phase.
Your Figure 1 (made in 2012) is a projection until 2016. I do not doubt tax subsidies are thought to be mostly “available to all firms". But in practice it is whoever lobbies (and campaign contributes) the most, gets the most. Precedence also plays a major role. Here is the breakdown by industry of tax subsidies for 2008-2010. I do not suspect it has changed much.
Notes: This does not include direct subsidies or direct sales; just tax breaks. Coal used for electricity generation is included in the “utilities, gas and electric “ category.
The source is the Citizens for Tax Justice in which has a bundle of other disturbing facts about corporate taxes - read them and weep for our country.
As far as removing these Oil/Gas subsidies increasing the cost of gas significantly, that does not compute. Take Exxon Mobil: they had $4.096B in tax breaks over 3 years 2008-2010 (see page 6 of the CTJ Report linked above). That is $1.365B/year. Their profits in those years were (could not find 2009). Their total assets as of Dec 2013 was . They have a lot of gall continually asking for tax breaks and subsidies year after year given their wealth. So if you really want lower gas prices, their continued overpricing is what you should complain about. Informal collusion on pricing abounds. Or be like me - try more gas efficient cars.
The rush of money to the corporate coffers, to the wealthy and to the financial sector is what is stagnating the economy. Piketty says that is the inevitable outcome of a long-standing capitalism (when return on investments is greater than the overall economic growth, capitalism malfunctions). He recommends a wealth tax to remedy. Keynes recommends government spending to create jobs when in a recession. Dodd-Frank could control the financial sector (if it ever gets implemented) to not allow highly leveraged, speculative investing that caused the financial crisis. Together they have the solution, imo. A third of a century of increased deregulation / lower taxation of the rich/corporations (i.e. supply side economics) simply has not worked for the majority of the American people and has fouled our environment/climate.