Hey, welcome to EVE!
Whether or not you can shoot depends on the security of the system you’re in.
1.0 to 0.5 you cannot shoot unless they’re either suspect (yellow flashing), criminal (red flashing), have a limited engagement with you (cyan flashing), or at war with you (red star flashing). Shooting any of these will allow them to shoot back though, so be careful! If you set your safety to yellow you won’t get accidentally concorded for shooting the wrong target, but you can do criminal actions that make you suspect and allow others to shoot you accordingly. Safety set to red means you can shoot people ‘illegally’ in highsec but concord will respond after a few seconds and destroy you (there is no avoiding this).
In 0.4 to 0.1 you can shoot anyone safely as long as you’re not on a gate or a station. Shooting someone you couldn’t legally shoot otherwise ( suspect, criminal or war target) will make you a criminal, so be careful. If you commit a crime (shoot someone) on a gate or a station the guns on that structure will shoot you back - they hurt, especially to smaller ships, but you can run away from them.
In 0.0 and lower (including wormhole space) you can shoot whoever you’d like with no repercussions.
In all cases, if someone is shooting at you already you’re legally allowed to defend yourself without concord intervention. However simply having a target lock on you is not enough.
The full timer mechanics are a bit more detailed but these are the basics you really need to know to get started. You can see more details on timers, safety settings , or more on just crimewatch mechanics in general from these links.