Are there any ways to mess with space and time?

Answer 1

"Time" is an abstract concept invented by and existing only in the mind of Man. If the universe was devoid of intelligence and there were no creatures to measure "time" it would not exist. Just as there is no sound if nobody is there to hear it like that proverbial tree that falls in the woods.
.
All that you know of, your existence, your being, and your sense of "time" is all within your mind. Every time you sleep your mind suspends "time" measurement. Take a nap in a moving car and in a sense your altering "time" and space at the same "time".
.

Answer 2

Of course. You take a heavy stone and swing it around in your hand. You just made a transmitter of gravity waves. It is a pretty poor transmitter but one that can be picked up if you have a sufficiently sensitive receiver.

These people are doing just that:

http://www.npl.washington.edu/eotwash/

Their stones are a bit more refined

http://www.npl.washington.edu/eotwash/experiments/experiments.html

but in essence they are creating periodic gravity waves and picking up the near-field solutions.

Now... the size of the effect might not be what you are looking for, but since you did not say how subtle an effect qualifies, these experiments answer your question with a clear "yes".

Answer 3

Some of the solutions to General Relativity 'kinda seem' to maybe imply that you could. But they also indicate that the energies required would be several orders of magnitude greater than that given off by an exploding supernova. So...... Probably not next week.

Doug

Answer 4

yes, very strong gravity or high acceleration will affect both.