Welcome to the community! Please see below for some answers:
1. You can edit or add CSS files to change styling in articles, for individual issues, and for the journal as a whole, right?
Yes, that's correct. Journal-level stylesheets can be uploaded by Journal Managers in Journal Setup Step 5.6 (or you can choose from a number of pre-loaded themes there as well). Issue-level stylesheets can be uploaded by Editors in the Issue Data page for any issue, under the "Cover" heading. Article-level stylesheets can be uploaded whenever an HTML or XML galley is uploaded. (You can't upload stylsheets for PDF files, of course.)
2. It seems that, according to this (viewtopic.php?f=8&t=4148), in order to make major changes (like deleting certain links) I would need to have access to the site template files. That would require administrative access, correct? And so doing such edits is impossible at my level (journal manager), correct? Furthermore, even if I could do this, can I make the changes for only one journal (there are multiple journals hosted by the university's library)?
To edit template files, you actually need server-level
access to the application files, usually via FTP or SSH. You can't get this kind of access through OJS itself -- that is, even OJS Site Administrators don't necessarily have server access. Template files are stored in different locations on the server. If your OJS system files are stored on the server in /var/www/html/ojs/, for example, you will find template files in /var/www/html/ojs/templates/; /var/www/html/ojs/lib/pkp/templates/; and possibly in various plugin directories (/var/www/html/ojs/plugins). At the moment, any change you make to the template files will affect all journals hosted in that install; so if your library hosts all journals from one OJS install, a template file change will be seen across all journals, but if your library installs a separate version of OJS for each journal, then this is not a problem. If you aren't sure which case is true in your situation, just send a link along and I can probably let you know.
3. Is there any way to change HTML on one of the pre-existing web pages? In this case, the editors want to put the words “In Press” underneath “Table of Contents” in the current issue page. The idea is to be able to put up articles as we get them finished, rather than wait until the end of the year to publish them. Is there a way to do this that doesn’t require administrative access to the template files? I’m sure I could jury-rig some sort of solution with CSS for each article, but I was hoping to be able to do something a little more general.
You should be able to do this. Take a look at the current issue's Issue Data page. (You can do this by logging in as an Editor; clicking the Back Issues link on your User Home page; clicking the current issue's title link; and then clicking the Issue Data tab link.) You'll find a "Description" field under the Identification heading. Any text you put there (including HTML-encoded text) will appear in the issue's public Table of Contents page. Unfortunately, it appears between the vol/issue title and the "Table of Contents" text, so not exactly where you want it -- to modify the placement you would indeed have to make a small template file change. But in any case, you can definitely link to items in that field, although the items (eg. pre-prints) will have to be publicly available online somewhere.
If you have any other questions, please just let us know!