OLED Screens are a sandwich of layers, it is really weird when touchscreen keeps working, but I saw it before. Replace the Complete assembly LCD/Screen and that will fix the issue.
Only if is 100% clean water you can let it dry, anything else will left residual materials that will start making contact between small components inside of your phone. Take it apart and clean it, if the tactic engine still not working, replace it, and if it still not working check the motherboard.
I don’t know your technical skills, but the short answer is creating a new administrator account and now you can change/reset password from your account. There is so many tools on the industry like a flash-drive to unlock your account, or the in the worst case, making a copy of your personal files and reinstalling windows.
Well, there is many of possibilities, not because is new it will work better, for example a computer of 3 Years ago with a core i7 processor will perform better that a brand new computer with a Celeron Processor. Also storage a SDD of 2 years ago will work faster than a brand new HDD 5400RPM. You need a geek talk to resolve all your questions.
Depends how gentle you are with the screen, most of the times you can remove the screen without see any extra damage, sometimes the crack just go a little bigger that you can not see it, and if you are not using the right tool and forcing too much , you can damage the glass and even damage the LCD Screen.
Parts from $0.20 to $25.00 each, depending from where you are ordering it, parts are not the problem, labor is the high cost, a good technician will charge you from $150 by hour and up just for labor.
There is so many possibilities like, water damage, damaged LCD/OLED, software bug or loose connection. You can start telling us more about when it started, so we can have an idea.