Can A 4TB SSD be Installed

Yes, you may install a 2.5" SATA SSD up to 4 TB, such as this compatible Crucial 4 TB SSD. (That's the model that I have in my L502x, though I chose 1 TB.)

I have almost the same laptop as you, since I have the 15" version L502x. With an i7 processor, and now with 16 GB RAM and an SSD, it still works very well.

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. (Repeatedly touching a metal case part is not sufficient mitigation with modern components.)

You should be able to free up space on your current drive with the following steps:

go to Settings | System | Storage, and click Show more categories. That will show you what is using the most space. On that same panel you can also run Storage Sense to delete temp files, etc, and you may configure Storage Sense to run automatically in future.

Also, do this:

1. Run Disk Cleanup
2. click the button Clean up system files
3. select your C: drive and select the various check boxes
4. click the More Options tab
5. under System Restore and Shadow Copies click Clean up button and click Delete button to confirm
6. click OK button
7. click Delete Files button.

That should free up a fair bit of space for you.

Note that applications are by default installed to your C: drive. Some applications take up a lot of storage. If there are any applications that you no longer need, you may uninstall them to free up space.