I think pretty all questions in your poste are answered in what James wrote. or in Gnatry docs.
If I edit the complied file, what problems can it cause?
you will loose that your modification each time you change a setting in the template.
Instead of changing css you should add css. You just need to create to create a file called [template-name]-custom.css in the css folder of the template. For Gantry this would be gantry-custom.css ... for Voxel it would be rt_voxel-custom.css.
Please note you don't need to work on LESS code. You can also just use CSS.
How do I know what LESS file to edit, if Firebug won't show me the path?
You should never add LESS or CSS-files of the template. Add your own CSS or LESS files instead.
If I can identify the correct file, can I just open it in a text editor, make the change and then save it.
You should never add LESS or CSS-files of the template. Add your own CSS or LESS files instead.
After doing some reading about LESS. Very little of which I understood, it sounded like I had to use a separate application to edit LESS files, is that correct?
That is not correct. You can use every text editor. But you don't need to use LESS.
Just use CSS if you are familiar with that.
At the end its all about copy and paste.
Copy the rule from Firebug.
Paste it into a custom css-file.
Add a little css specificity.
For example: #rt-bottom should become div#rt-bottom