So far I love Webwork! It is awesome!
I noticed that an admin can edit questions when making homeworks.
Are these edits temporary or permanent?
(i.e. Do the mods only pertain to the current homework?)
The edits are permanent (e.g. if you select "Save AS [TMPL]/...") but local. In the standard set up, a prof in a course does not have permission to edit problems in the copy of the NPL sitting on the server. You could use the edited problem in other courses by using the File Manager to copy the edited pg file to another course's templates directory.
If it's a change you think others would welcome, use the "report bugs in the problem" button (it doesn't have to be a bug) to suggest the changes be added to the problem in the master copy of the NPL that is distributed to everyone.
Hope this answers your question.
The original (if it is the NPL) is never touched as you (normally) don't have permission to edit it. If you do your edit and select "Save" you will get an error message telling you to save a local copy using "Save as". If you are trying to edit a problem that's already in the course's templates directory (so you do have permission to edit it), you can use "Save" which changes the original or "Save as" to save the new version and keep the original.
When using "Save As" which saves your new version, you have three optional things you can do: (1) and replace ...,(2)and append to end of set ..., (3)as a new independent problem. The first replaces the original version by the new version in the student's assignment. The second keeps the original version in the assignment and also adds the new problem to the end of the assignment. I think the third is just the default action, which saves the problem but does not assign it to students. You can then use the Hmwk Sets Editor to assign the problem if you want.