Yes, displaying or performing copyrighted photographs and music for classroom purposes is allowed under section 110 of U.S. Copyright Law. (U Minn)
Yes, changes made to enhance your instructional purpose, e.g. commentary, criticism, even parody, are activities allowed under the fair use provision. (U Minn)
Under certain conditions, purchased or rented pre-recorded video programs may be used in the classroom. Section 110 (1) of the copyright law enables teachers to use (perform) such a video without a public performance license (which is normally required whenever a video is shown outside of the home). The conditions which must be satisfied are: 1) the use must take place in a non-profit educational institution, 2) the use must occur in a classroom or similar place devoted to instruction, 3) the use must be part of a regularly scheduled course (thus ruling out extra-curricular or recreational use), 4) the use must be exclusively by the instructor and the students in the classroom, in the course of face-to-face teaching activities. (UC Berkeley)
Up to 10% or 3 minutes, whichever is less, in the aggregate of a copyrighted motion media work may be reproduced or otherwise incorporated as part of a multimedia project. (CONFU)
Works residing on a site that makes no mention of copyright should be presumed to be copyrighted; just because something is freely available on a website does not mean it is in the public domain. If a work is published online with a statement that it is in the public domain, you will have to judge whether or not these claims are trustworthy, keeping in mind that such claims will not protect you should a copyright holder object to your use.
You may encounter works online for which the author or creator specifically grants rights to use them, such as those released under a Creative Commons license. A Creative Commons license allows you to make certain uses of a work without asking for permission, provided you follow the terms set by the creator. (U of Mich)