Nope. Gravity does not work like this. The Sun's gravity is pulling Mercury, but the planet is traveling so fast that it can't fall fast enough to ever hit the Sun. Mercury's orbit is elliptical though, so it does vary in distance from the Sun. As it gets closer to the Sun the pull from the Sun's gravity does increase, but so does the orbital velocity of Mercury, which means it simply keeps on moving in its orbit. As the orbital radius increases and Mercury gets further away the strength of gravity decreases, but so does Mercury's orbital velocity. The end result is a stable orbit.
It is actually VERY difficult to make something crash into the Sun. If we were to suddenly reduce the Earth's orbital velocity by 20% we would simply move into a much more elliptical orbit. We would not fall into the Sun. If we wanted to send a space probe to the Sun we would have to completely counteract the orbital velocity it has from being launched from the Earth. This takes something like twice the fuel as it does to send a probe out of the Solar System!
Have no fear, Phinds's bark is worse than his slimy, gummy bite. However, he is correct. A study on the math of gravity would immensely increase your understanding of how it works.
First, let's dispel this notion that they are "only theories". Newtons Law of Universal Gravitation and Einstein's Theory of General Relativity are indeed "only theories". However when said like that it implies that they really have no idea what they are talking about, which is completely incorrect. They are both Scientific Theories, which is different than your everyday usage of the word "theory".
From here: http://en.wikipedia.org/wiki/Scientific_theory
A scientific theory is "a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment."
The key here is "confirmed through observation and experiment." Both theories above are legitimate scientific theories that have mountains of evidence in their favor. And yes, we know that Newton's theory is "wrong". However, it isn't about right or wrong. It's about accuracy. We can never truly know whether a theory is right, we can only say that it predicts real world effects with a certain degree of accuracy. And Newton's theory is so accurate, even though it's wrong, that we still use it to fly spacecraft to other planets.
This is pure nonsense. We haven't been able to manipulate gravity yet because none of the 4 fundamental force of nature, including gravity, are capable of being "manipulated" in the first place. It's like saying we should be able to increase or reduce the charge of an electron. Well sorry, we are made of the things and the fundamental properties of particles are not able to be changed. And I would bet my paycheck that they never will be. If they could then the universe would be far different and we probably wouldn't be here today.
How can one change the rules that one must play by in the first place?
Not true. I don't know anything about this "fragmented evidence", but it's probably been fragmented by the mountain of evidence in favor of General Relativity crashing down upon it. And since our most accurate theory of gravity is GR, not classical gravity, any resemblance between electromagnetism and gravity is ignoring the last century of scientific advancement.