Can I set properties on everything in the repository, then apply the properties to every new file coming into the repository?

Subversion will not change a file's contents by default; you have to deliberately set the svn:eol-style or svn:keywords property on a file for that to happen. This makes Subversion a lot safer than the default CVS behavior, but with that safety comes some inconvenience, as you cannot apply these properties to incoming files.

To set properties on all files already in the repository, you must run svn propset on every file (in a working copy), and then svn commit. Scripting can probably help you with this.

Unfortunately, there's no server mechanism to automatically set properties on files being committed. This means that all of your users must remember to set certain properties whenever they use svn to add a file. Fortunately, there's a client-side tool to help with this. Read about the auto-props feature in the book. You must make sure all your users configure their clients' auto-props settings appropriately. You could write a pre-commit hook script to reject any commit which forgets to add properties to new files. See the link below for more information.

However, this approach may be overkill. If somebody forgets to set svn:eol-style, for example, it will be noticed as soon as somebody else opens the file on a different OS. Once noticed, it's easy to fix: just set the property and commit.

Related information
See an example on how to check mime type on commit.