Why is my old MacBook Air working very slowly, taking 20 minutes to boot and 5 minutes to open apps?

Before you do anything else, you need to back up your data.

It appears there may be a problem with the SSD. It's entirely possible it's on its last legs. I'm not seeing anything in particular that would indicate a software related problem.

The next stop is to start looking at replacing this machine with something new. Your Mac is obsolete. It can no longer run a supported version of macOS. Apple no longer offers repair services for that model.

It had a good life. It's time to let it go.

I don't see anything in particular either although something is causing the laptop to hang.

Try running Disk Utility First Aid on the hidden Container. Within Disk Utility you may need to click "View" and select "Show All Devices" before the hidden Container appears on the left pane of Disk Utility. Even if the First Aid summary says everything is "Ok", click "Show Details" and scroll through the report to see if any unfixed errors are listed. If there are errors, then run First Aid again until the errors are gone. If the errors remain after several scans, then run First Aid while booted from Recovery Mode. If after several scans the errors remain, then the only way to fix the file system errors would be to perform a clean install of macOS by first erasing the whole physical SSD followed by reinstalling macOS & restoring from a backup.

Make sure to also disconnect all external devices in case one of them is causing a problem.

Do you have a backup of the data on your computer? If not and you have any important files, then make sure to make a backup immediately so you don't lose those important files.

Download Etrecheck and post the report it generates here.

This will help greatly in diagnosing what's causing the problem.