Is there a way to change the default settings for users within Jira? For example, by default, a non-Admin user (a developer, for example) has access to all projects rather than to (only) their assigned projects. Or, is this something that has to be done by an Admin when a new user is created?
I've read about permissions, schemes, etc. but I'm having a difficult time figuring this one out. (I'm not a programmer...)
Yes, JIRA schemes take a while to get your head around. The way to do what you're asking is to change the group that goes into the project role "Users" for your project. Usually this role is filled by the jira-users group but you can change it to be any JIRA group you like. So define a JIRA group "special-people", add the users who should be able to access the project, change the project role Users to use the new group and there you are.
There's more detail at my new JIRA Development Blog in a recent article and in the Atlassian documentation
~Matt