MacBook Pro overheating with fan running excessively

Based on your EtreCheck test results, there appears to be some adware installed named WebTools. WebTools is a tool used to bypass macOS security measures.

• To uninstall this, select Finder and select "Go" > "Go to Folder" from the menu bar, or press Shift-Command (⌘)-G.
• Paste "~/Library/Application Support/" into the search bar and select "Go".
• Scroll down until you see the folder named "WebTools".
• Right-click on the folder and select "Move to Trash"
• Empty your trash

If the problem persists, consider resetting the SMC. (https://support.apple.com/en-us/HT201295)

That is correct. The battery needs to be replaced for your Mac to hold a full charge. Below is a link for one:

https://www.amazon.com/BRTONG-Laptop-Battery-MacBook-Version/dp/B0827L2NYL/ref=sr_1_7?dchild=1&keywords=mid+2012+macbook+pro+battery&qid=1595369995&sr=8-7

Run the Apple Diagnostics (sometimes you won't be able to access the online diagnostic servers).

Run EtreCheck and post the report here using the "Additional Text" icon which looks like a piece of paper.

Try using the Activity Monitor app to see which program is causing this issue. The box on the bottom of the app is your CPU load indicator, and it should be below 40%. There should be a list of programs running. If any of them have an abnormally high CPU usage, that might be the culprit. If everything in Activity Monitor is normal, consider resetting the SMC, as that is responsible for fan control.

Apple's documentation is sometimes incorrect or incomplete. A 2012 model can in theory connect to the online Diagnostics using the "D" key or "Option + D" keys, but they need to have had macOS 10.12.6+ installed so that the system firmware has this ability. However, Apple did break the ability to boot to the online diagnostics with some of the system firmware versions.

As mechanical hard drives age, they tend to start failing as the moving parts inside such as the head and spindle start to wear out. This is expected of older hard drives. Luckily, this can easily be resolved by swapping your drive. I highly recommend switching to a Solid State Drive (SSD), which contains no moving parts, meaning it will not only be more reliable than conventional hard drives but several times faster. SSDs can be found online or at retail stores for a reasonable price. Your Mac supports 2.5" sized SSDs, with the storage capacity depending on how much data is on your Mac. For data transfer, I would use SuperDuper, which is free software that will clone your hard drive onto the SSD. Installing the SSD into your Mac is also relatively simple. I have provided the links for everything you will need below.

Western Digital 2.5" SSD:

https://www.amazon.com/dp/B073SBQMCX/ref=sspa_dk_detail_0?pd_rd_i=B073SBZ8YH&pd_rd_w=SF3nn&pf_rd_p=48d372c1-f7e1-4b8b-9d02-4bd86f5158c5&pd_rd_wg=YHd1F&pf_rd_r=32M2VBFGY8G5JMTDB3ZJ&pd_rd_r=f7fb43ca-8d7e-4e68-9104-33f30f48d1cb&spLa=ZW5jcnlwdGVkUXVhbGlmaWVyPUEzQ0RYV1BSQk1OTTZBJmVuY3J5cHRlZElkPUEwMjQ5NDk5MzA5TFdZSFJWTk1CWCZlbmNyeXB0ZWRBZElkPUEwMzQ0NzYyMUNLTERNRlJCMzZMMiZ3aWRnZXROYW1lPXNwX2RldGFpbCZhY3Rpb249Y2xpY2tSZWRpcmVjdCZkb05vdExvZ0NsaWNrPXRydWU&th=1

SATA III (Hard drive/SSD interface) to USB adapter:

https://www.amazon.com/Drive-Adapter-Cable-Support-Black/dp/B07S9CKV7X/ref=sr_1_3?crid=2AWSPMDD90P3Z&dchild=1&keywords=sata+to+usb&qid=1595366691&s=electronics&sprefix=sata+to+%2Celectronics%2C172&sr=1-3

SuperDuper software link:

https://www.shirt-pocket.com/SuperDuper/SuperDuperDescription.html

(There will be a download option for free on the right portion of the website under the "Download Now")

SSD installation guide:

https://www.cnet.com/how-to/upgrade-your-macbook-install-ssd-hard-drive/

You can use MalwareBytes to remove the Adware.

I also would uninstall the Symantec/Norton software since anti-virus and third party security software is not needed on a Mac and usually causes more problems than it solves plus it impacts system performance. I'm not sure about macKeeper, so I will leave that to other more knowledgeable contributors.

If you want to check the health of the hard drive you can do so by running DriveDx. Post the DriveDx report here using the "Additional Text" icon which looks like a piece of paper. If you are still using the original Apple hard drive then it is very likely beginning to fail or it is just wearing out.

The hard drive SATA cable in this particular laptop has an extremely high rate of failure especially when using an SSD so if you decide to upgrade to an SSD you should also replace this cable. Upgrading to an SSD will definitely increase system performance. 4GB of RAM is not very much these days so adding a single 8GB module can help a small bit as well. If you decide to upgrade the memory, then I would suggest purchasing a single module and keeping one of the original 2GB modules so that would give you 10GB of total RAM. Since Macs are very picky about the memory used it is recommended you purchase memory from Crucial or OWC for best results.

Normally a "Service Battery" condition indicates a hardware issue has been detected within the battery, but I'm not sure if the recent macOS changes to battery health management may have changed this. You can still get an official battery replacement through an Apple repair since this laptop is still supported by Apple.