Is the major reason that we have trouble with nuclear power the inability to shut down the reactor? Like a major malfunction preventing the control rods from settling into the core?

When the fuel rods begin to melt down can they be stopped from reacting if you were able to get the control rod material to the fuel rods?

Is it possible to develop the elemental material in control rods into some sort of powder or liquid form that could be injected into the core if the control rods fail to shut down the reactor?

Could the core be designed in such a way that it could be literally and violently pulled apart in order to get control material on the fuel rods and 'neutralize' the reactions? Or would this make a critical situation worse?

Finally has anyone ever come up with ideas like these?

The premis of the question is a bit flawed. Like with what is happening in Japan right now its not really about the reactors its about the ponds that held the waste from the reactors. There are going to be a lot of lesons learned from this disaster.

As far as your ideas many have already been addressed. The new technology is much better then it was 30 to 40 years ago. Think of how cars were then vs cars now and you get the idea. The main problem that has to be dealt with is cooling. And in this case (Japan) all the back up systems failed. If any one of them would have remained in tact then we wouldn't be looking at what we are as of today.

Well I guess so, from an engineering standpoint, you can't expect tall buildings in Manhattan to still be standing when the designers never thought of commercial airliners being used as missiles. Nor can you expect an overpass to stay in one piece when the designers didn't have the foresight to predict a tanker filled with gasoline could explode on top of it. It's Tragic when an unsinkable ship hits an iceberg puncturing enough bulkheads that the ship pulls itself down under.
I guess that goes for Nuclear power plants too when it gets hit by an earthquake with magnitudes 2+ greater than it was designed for, then it gets hit by a tsunami, I guess that's an SOL kind of day.
I'm optimistic that we will learn from this incident. But it is so unfortunate that the most well learned lessons are taught from tragedy.

That's the same thing with experience. It's through experience that you learn your lessons better :)

And above that, it's only through your own experience that you learn best.

The problems with nuclear are monumental when they go wrong. The waste will always be an issue as well. Renewables are the future.