Can anyone attempt to send a rocket into space? Or are there designated launch pads and clearance times?
You should inform your local air traffic control and get airspace clearance for the launch. You should probably do it very publically as well otherwise some slightly paranoid nations may take it as a threat.
You probably don't want to bother unless you are near the equator though (less energy is required to launch from there). You also want to launch when air density is at a minimum if possible.
From a practicality POV, most space launch vehicles are very over-engineered. It's cheaper to lose a few cheaper ones than to build better quality ones (unless they have a live payload) so there are logistics to consider as well.