What can I do to fix my PC issues?

My Sony VAIO PC has been giving me a bit of trouble with the screen going blank while I'm using it forcing me to restart it and now after being fine this morning I go to turn it on and it says "no operating system found" so I check the hard drive to make sure it's in place and now when I turn it on the power indicator is green like if should be but the screen stays black and it doesn't start up… Also I'm not sure if this is relevant but I feel like it gives me more problems when I connect my iPhone as a hotspot or a portable mouse USB

If your PC had been booting up properly then your Wi-Fi hotspot problem could have been of concern. But since screen remains blanks on boot-up. Sounds like your PC is getting overheated which is causing it to freeze and non-responsive. Try cleaning out the dust from its vents.
any further help can only be provided if you elaborate on what errors you are getting and when

Unplug & remove the battery before doing anything.

General housekeeping - get a can of compressed air & a vacuum cleaner with a hose. Set up the hose by the exhaust vent on the computer. Turn on the vacuum. Fire several short bursts of compressed air into the intake air vents to loosen dust & crud. The vacuum cleaner hose will get it so it doesn't get back into the computer.

Get a piece of gauze or pantyhose to put over the vacuum cleaner hose. Use compressed air in one hand to loosen "stuff" under the keys on the keyboard - the vacuum cleaner hose in the other hand will pick up the skin flakes, crumbs, dust, etc.while the hose or gauze keeps any loose keys from being sucked up…

Use high proof rubbing alcohol on a microfiber towel to wipe the screen, keyboard, and laptop case down (it might not do anything - but you're cleaning anyway - might as well get it ALL).

Press & hold the power button for twenty or so seconds (no battery and not plugged in still). You're cleaning the RAM so that it doesn't remember what went wrong the last time it tried to boot up.

Try turning it on to see what happens.

If you have an Ethernet connection to use - try that to get any updates to install - as wireless connections sometimes lead to corrupted downloads on updates. A corrupted update is worse than no update at all for causing problems (which is why I have a docking station with an Ethernet cable at my main desk at home).

If you have a recent recovery image backed up to an external hard drive, flash drive, or burned to optical disks - a factory image recovery followed by updating everything using an Ethernet cable connection might give you a more stable computer to put your personal information back on, using the back up.

If you don't have a back up - see if you can get the computer up & running long enough to make one before trying anything else. If you have never made a set of recovery disks - try making one NOW - because if the hard drive is starting to fail, you will really want a set of factory image recovery disks to set up a new hard drive and a recovery image of your personal files & photos, as well as other software that might be installed, to get back to where you are NOW instead of loosing stuff if the hard drive crashes on you.