If the paper is not being pulled into the scanner from the document feeder then it is probably dirty rollers. You can use rubbing alcohol on a lint free cloth to clean the rollers. You do not need to lubricate the rollers.
This is probably a driver issue. You can test this by connecting headphones to the laptop and listen if you get the same audio problem. If you do then the best way to update the drivers is to go to Lenovo - Support and download the current driver. If the head phones do not have the same problem then it probably is the built in speakers, you can get information on part numbers at the same Lenovo -Support site.
It looks like the magenta or yellow print drums are failing to clean between pages. This can also be caused by dirty contacts in the printer or the print drums. You can try cleaning the contacts with a lint free cloth. If the print drums are old then it may be better to replace them.
If you mean you cleaned the thermal grease off of the processor and gpu then if it was not done right it would lead to overheat conditions. You should run the Dell diagnostics, restart computer and press F12 to bring up the menu and select diagnostics. The SSD you installed may be the cause of the power change, diagnostics should help with that.
You can clean the battery alkaline leaks with white vinegar on a cotton swab. If the battery was removed shortly after leaking then the amount of alkaline residue should be small and not too much damage to the contacts. The cotton swab should be damp and not dripping wet, the vinegar acids will neutralize the alkaline residues. Be gentle with the contacts but make sure that they are clean and the wires are intact. You can follow the vinegar with isoplyl alcohol to clean up left over residues.
If the software is running normal then the CPU may have gotten hot enough to be damaged. It depends on how quickly you shut down and how long the CPU was at 190+ if there is damage. I would suspect a DLL or other file to be using up CPU time and causing the lag. This could happen if you shut the computer down manually instead of the OS shutting it down. You should replace the fan as it is not going to get better. You should also clean and reapply thermal grease to the heatsink and CPU. You did not specify an OS, but for Windows you can use Task Manager to see which routines are running, you can also use Resource Monitor to find out if there is an application or DLL that is causing the lag.
The update may have replaced the drivers for the touch screen. You should try going to www.lenovo.com and look for support for the model of your laptop. If there is an automated support tool to check for drivers then use that, if not then search for a driver that fits the description of touch screen display. You will need to install Lenovo’s installer to set up the driver update.
Yes, that is weird that the temperature gauge shows hot when the heater fan is on and you are going uphill or over 50mph. The heater is linked to the engine cooling system and it should transfer heat from the engine to the passenger compartment and reduce engine heat. My guess is that it may be a faulty sensor, loose or dirty connection on the sensor or the gauge. You did not mention if your garage checked the sensors or the cooling system, try going back and have them check the cooling system and sensors/connections.