Maybe liquid damage? It's fairly common. If not, it's also fairly common for them to just give up every now and then. The good news is that they are fairly easily replaceable. Keyboard screws are usually located under the battery (actually in the battery void). There may also be one or two on the bottom casing and you may also have to remove the uppermost panel on the keyboard side (between the keyboard and the hinges). Screws that hold the keyboard panel in place are clearly marked with a small keyboard symbol. You can usually find a guide on YouTube (even if not the same model, you'll get a good idea how they fit together and I haven't come across any that are too dissimilar) or you can see if your model is on ifixit. Most of these Toshiba Satellite models have keyboard replacement tutorials (haven't checked them all but they should do) Once the keyboard is out its a case of disconnecting the ribbon cable and installing a new one. You can usually find them on eBay pretty cheap. Hope this helps!
This is unfortunately a fault that can only be solved by replacing the LCD/digitiser assembly again. It may just be a faulty part (I find them very hit and miss) or it could be that the flex got bent/crimped during installation. They are very fragile and don't take a lot to damage. It might be worth removing the screen again to disconnect and reconnect the digitiser zif connector in case there's something wrong with the contact between plug and port. Personally though I think it sounds more like a digitiser fault
Unfortunately, sometimes it is irreversible and it sounds like you have done pretty much as much as you can. Some say rice shouldn't be used as it can deposit more minerals than just water itself (starch etc.) which can contribute further to corrosion. Personally with a water damaged device I would tear it down as much as possible and use a combination of Isopropanol 99.9%, time (to dry naturally) and patience, remembering to avoid putting power through any part of the device until you can be fairly certain no moisture remains.
This is a fault with the power/volume/mute flex invoking random presses. The only real fix for this is to have the flex replaced. I have done lots of these but it isn't a job for just anyone as it requires almost a complete teardown of the phone. However, the part is very cheap and if you know someone that can do the work it shouldn't cost much despite how big the job sounds. For someone that dissembles iPhones regularly it is a run of the mill job
Have you tried a hard reset? Press the two buttons on the back of the camera with a green dot by them. For the 5100 they should be "Menu" and "Information". My D5300 does this sometimes but I know what causes it - I have a portrait battery grip and when the tripod is hooked up, if I pick it up by the camera (and not by the tripod), the weight of the tripod pulls the grip downwards and interrupts the battery connection, so the camera has shut off without powering down. This may be irrelevant to your problem but it's worth knowing. It could just be that you shutter has reached its end of life. You can check the life expectancy of the D5100 shutter here
I can't find the Dell model you have. Are you sure it's correct? In any case, (presuming it is a laptop), DVD drives are easy to replace and are usually only secured by one screw on the underside of the casing and it should just slide out (screw hole will be labelled too). They're not usually very expensive either. DVD drives are not usually very serviceable and once something goes wrong with them the best solution is often to just replace the drive
Go to settings>>applications>>all, find the keyboard you are using and clear the data and try again. If the problem isn't resolved, install a third-party keyboard and see if you have more luck that way.