I have two questions about defamation liability. If I'm quoting what another person said
about someone -- am I still liable for it?
If the negative quotes are about a celebrity who already has a reputation
for being crazy and difficult to work with...does that lessen the risk I'm taking
in publishing them?
You haven't said where you're located, or where you'd be republishing the other person's comment, so that makes it impossible to give you any clear guidance. As has been pointed out, defamation laws vary considerably from nation to nation.
In the U.S., generally speaking: (1) to defame what the law calls a "public figure", which would include most celebrities, you have to say something that is factually false and do so with "actual malice", which means either you know the statement is false or you published with reckless disregard as to whether it's true or false; (2) a statement of pure opinion is not actionable, but an opinion that can be reasonably interpreted to imply a false fact is; and (3) if the initial publication of a statement is actionable, you can be liable for republishing it unless you have either (a) a legal "privilege", for example, you're testifying in court or you're a reporter relying on a public document or official, or (b) the authorization of the original publisher, for example, if you interview someone and he/she says "you can quote me on that".
It's relatively easy to research theses issues on the web. A lot of attorneys and law firms have posted pretty good discussions of the law in an effort to demonstrate their expertise and to attract clients.
All that being said, as with any legal case, the likely outcome can be very fact specific, and this is not legal advice (especially since you've given so few facts). Check with a lawyer in the jurisdiction(s) where you publication will appear.