Can I know if my mobile phone/computer camera has been hacked?
Honestly these days it is not very likely that you will notice a hack unless you are installing from untrusted sources or have rooted (or jailbreak for an Apple device) in which case the sophistication of the malware is not enough to hide all the usual tell-tale signs (slowness, new applications, etc.).
For a targeted hack and in many cases mobile malware, you will almost never know unless you are very closely monitoring network traffic for your devices.
Very often though for webcams, the light will at least come on, but that isn't always true and having a cover is best to be safe, no matter what.
If I was hacked, does putting duct tape over camera/webcam really prevent them from watching me? Can they watch me through the screen?
Yes. Though it may not prevent them from listening to you (as most webcams have microphones embedded in them). Also, again, use a real cover and not tape. This ensures that they cannot even see shadows given your tape, paper, etc. is thin enough.
I'm not entirely sure where you got the idea they can watch you through your screen, because a LCD/LED screen modulates light for output. That being said, an attacker can extract passwords, fingerprints, memory, and install a keylogger which is worse than staring at your person.
Mobile security is not only still an infant in the infosec world, but it has the unfortunate problem of being widely accessible, with many options due to a plethora of manufacturers and a wider variety of users at a price point that makes them easily replaceable. The desktop and server market, while older, still suffer from the expanding scope that is our technological world.