If you use material on your web site, the copyright to which belongs to
someone else, you will need to either (a) obtain a license
(permission) from the copyright owner; (b) determine that the source
material is actually not "copyrighted" and is in the public domain; or
(c) determine that your use qualifies as a "fair use" under copyright
law. Any use outside these three will expose you to liability for
Fair use contemplates that you ARE infringing copyright--the doctrine
simply gives you a defense if you get sued. Basically, you are
infringing someone's copyright in any content of which you are not the
actual author that you reproduce in your site.
Under US copyright law, the Fair Use Doctrine, found at 17 U.S.C.
Section 107, holds that no permission is needed for purposes such as
criticism, comment, news reporting, teaching (including multiple
copies for classroom use), scholarship, or research, SUBJECT TO THE
(1) the purpose and character of the use, including whether such use
is of a commercial nature or is for nonprofit educational purposes;
(2) the nature of the copyrighted work;
(3) the amount and substantiality of the portion used in relation to
the copyrighted work as a whole; and
(4) the effect of the use upon the potential market for or value of
the copyrighted work.
So, to answer your question, you have to first ask if your use falls
into one of the enumerated categories [criticism, comment, news
reporting, teaching (including multiple copies for classroom use),
scholarship, or research] AND THEN you have to apply the four factors
and see if more of the factors weigh in your favor. Thus, it is
difficult to opine here as to whether your uses fall within fair
use--it is a fact-sensitive determination you must undertake with each
new use of the material you take from another site.
The most risk-averse and legally sound course is to contact the
copyright owner and obtain a license (permission) to reprint their
pictures on your web site.