I'm citing my sources, so I don't need permission to include excerpts from them, right?
Attribution is separate from permission. You of course need to cite your sources, but this is separate from the question of whether you need a rights holder's permission to include excerpts from or copies of those sources to begin with.
As a copyright holder, the author has exclusive rights to (among other things) reproducing the work. If you want to reproduce still-in-copyright work in your dissertation, you'll need to decide whether it's fair use or get the copyright holder's permission.
Is it in the public domain if I find it online?
Do I need permission to link to content rather than include it?
I was the author of the work I want to use, so do I still need permission?
Am I allowed to make multiple books/articles out of my dissertation?
Keep in mind, though: If you publish journal articles that are merely excerpted from your digital project without modification, you should be careful about assigning copyright to the journals. If you later wish to reuse the same language in, say, a manuscript for a book, you don't want to have transferred your rights to that iteration.
If it was fair use to publish a work in my dissertation, is it fair use to publish it in my first book?
For instance, one of the fair use factors takes into consideration whether your use is for non-profit educational purposes. Once you begin publishing a book and earning royalties, the commercial nature of the endeavor may weigh against fair use for that factor. You'll need to undertake Step 1 analysis again in its entirety when it comes time to publish your manuscript commercially, and determine whether you need permissions.
Keep in mind, too, that your publisher may--as a matter of policy, to protect itself--want you to obtain permissions irrespective of whether you believe use would have been fair without permission.
Are unpublished archival materials protected by copyright?
Unpublished works subject to copyright protection. However, the duration of copyright for unpublished works can differ based on whether they are signed, anonymous, etc. For more on copyright length for unpublished works, consult the discussion of Unpublished Works (Ch. 3.2.1) in Peter Hirtle's Copyright & Cultural Institutions book; see also 17 USC §§ 302, and 303.
Keep in mind, too, that while unpublished works are not excluded from your use as fair use, what constitutes fair use of unpublished works may construed more narrowly by a court.
Are unpublished foreign works protected by copyright?
The length of protection in the U.S. for unpublished material is the same regardless of where the work was created, or what nationality the author was (17 USC § 104). If the copyright term for the unpublished work has expired, it's in the public domain for purposes of publishing your dissertation in the U.S.
How long are published foreign works protected by copyright?
The more complex answer is that, for foreign works: Based on the nationality of the author and place of publication, one can calculate whether the foreign material has entered the public domain. Though, you don't have to--you can use the wonderful Cornell University Public Domain chart prepared by Peter Hirtle. Check out the section "Works First Published Outside the U.S. by Foreign Nationals or U.S. Citizens Living Abroad."
I'm having trouble making a fair use decision. Can you help?
Will publishing my dissertation open access immediately, with no embargo, affect my ability to publish other works based on it?
Note that this is untrue for the majority of publishers.
Ultimately, you should check with your advisors and the guidelines of the publishers you are considering. It is important to familiarize yourself with the policies in your field.