Running fast: if you expect your legs to look like roadrunner's legs, they will.

Die in dream: whatever you expect to happen will happen. If you expect to go to heaven, you'll go to whatever your mind expects heaven to be like. If you think you'll cease to exist, I couldn't tell you what'll happen.

Piano: if you can imagine it, you can do it. Your experience would probably be limited since pianos can't see.

Time alteration: You can slow down time in a sense, e.g. making everything go really slow compared to you. I believe it's commonly accepted that you can't slow down "real time," or in other words dream for 15 hours but only have slept 6. Some people do say their dreams feel like they take longer than the time they're asleep.

Creating a sense: if you can think of it. Some people who believe in astral projection claim that on the astral planes you can sense things that your mind can't understand and it really messes with you.

Cloning: a book I have suggested things like this. It would be quite an exercise of the imagination, and possible if you could imagine what it would be like (and maybe even if you couldn't).

Studying: You might be able to if you've looked at all the pages you'd need to read. Your subconscious can remember stuff like that really well, but some people say you can't read in dreams (the text gets messed up). I haven't found that to be the case, but I still wouldn't depend on dreams to get good grades.

Shared dreams: Some people would say you don't need the electrodes to accomplish that. Some would say it's impossible no matter what. No one can really prove it either way, but it's always exciting to try.

Basically you can do anything you can imagine if you have good control and visualization power. There are very few limitations in lucid dreaming.