Is it possible to copy all my applications from the applications folder onto an external, format my mac, reinstall OS X and finally copy the applications back into the applications folder for installing them? Will that work? I am asking because my dr

It might work, but likely not. Why not simply backup the computer using Time Machine then format the drive and restore your apps from the Time Machine backup, heck of a lot easier and dead simple to do.

Question: if your drive is almost full, why go through all of that? Why not just move space hogging things such as photos, videos, movies, etc to an external drive to create more space on the internal drive?

Or you could get an external SSD sized to meet your needs, now and future, and boot from it. That way your internal drive can be available for data storage only or as a stripped down (no user data) standby bootable drive.

Does not work that way for most apps. I tried this once but the required OS files do not copy over.

Why not just upgrade? 😃

A MacBook Air (M1) is technically more powerful than your setup.