Of course it is a viable option. But in the real world it does not happen.
Mostly not, but this has a lot more to do with our corrupt and inefficient method of corporate governance than it does economics. The government shouldn't make choices about what tax rates to set based upon such things.
If corporate taxes are raised, and prices go up, consumers will either pay the higher prices or stop buying the goods. If they stop buying the goods, price pressure will force leaner profit margins and, yes, lower executive pay. I don't see what the problem is here.
If the government increases the fuel tax rate, your pump price will go up by that amount. It is that simple.
Sorry, it isn't that simple. Price competition between different providers practically guarantees this. There are a wide variety of factors that determine what I'm charged at the pump; there is no linear relationship between taxes and prices at all, which seems to be what you are positing here.
I will say that your mantra is quite, quite popular with those who are looking to justify the continual lowering of corporate tax rates. But your arguments do not follow logically or economically.