Several Librarians contributed to this answer

1.
I assuming since you are a student you have access to their university libray's resources. By "materials challenge", I guess you mean people challenging an item the library owns, e.g. censorship/intellectual freedom issues.

I don't know of any case studies offhand about materials challenge offhand, but I would suggest you look for books in your own university library's catalogue, "Library administration -- case studies" . I did a subject search under this heading in RedLightGreen and got these results.. http://www.redlightgreen.com/ucwprod/servlet/ucw.servlets.UCWController?ACTION=LimitWkLsRslt&BY=Subject&TERM=LIBRARY+ADMINISTRATION+-+CASE+STUDIES&MAXRECORDS=20&lang=english&MAXMATES=100&RSLTID=1&FROMRSLT=1

Also, check under the subject heading "Library administration -- periodicals". Often management case studies are published in journals.

If you have access to an online LIS database such as LISA or LibraryLiterature, you can try doing a keywork search for: "case study" and (censorship or "intellectual freedom")

Another subject search you could try, in either their catalogue or online database, would be the heading "Libraries -- Censorship -- Case studies" or even just "Libraries -- Censhorship" might have some good results.

2.
This seems to be an extension of another question, which deals with challenges to library materials that are really attacks on "populations identifiable by language and culture"--e.g. the recent fight over fotonovelas in Denver, which turned out to be an anti-immigrant campaign.

3.
Library Literature database gets 5 hits for the search: censor* and challeng* and polic*

Maybe it's better to look at all 90 hits for the search:
censor* and challeng* (to make sure you don't miss stuff that was indexed more broadly - or where title words were different, etc.)

Lexis Academic / Legal Research / Law Reviews is a good possibility - to hopefully get discussions of how libraries' policies affected actual legal cases. The search "past five years": (challenged books or challenged materials) and (policy or policies) got 18 hits. "Law Reviews" searches full text only - there is no way in Lexis Academic to limit to subject headings or titles (No doubt the very expensive commercial Lexis-Nexis allows that). The "past five years" search: (library or libraries) and (challeng! book! or challeng! material!) gets 30 hits; librar! and (challenged books or challenged materials) gets 13 hits.

"All avail Years" search: librar! polic! and (challenged books or challenged materials) gets 4 hits, back to 1983. Once again, maybe a broader search is safer: librar! and (policy or policies) and (challenged books or challenged materials) gets 38 hits in "all avail years".

In summary, this is for certain a candidate for commercial databases at a college or university (on-site if you are not a currently registered student). A web search would be pretty risky - or extremely time-consuming to weed out the passing references - and scholar.google.com will get you lots of links to things that are unavailable without a subscription or credit card payment (or student/faculty off-campus password access).

However, if you can't get to a library or get off-campus access, we can try to come up with a workable web search, using site:edu , site:gov , site:ac.uk , etc. to weed out some of the problem hits.