Depends on what you mean by the word "publish" but for these purposes, I'll assume as a book for the purposes of profit to yourself.
For your first question, Yes you can, so long as the Clans, Apprentices, and Warriors are not similar to the the ones featured in Warriors by Erin Hunter. Avoid similar names, similar customs, cultural values, and other identifying features where-ever possible.
For your second question, I'm assuming this is an original character who lives and/or works in the fictional setting of the 2016 film Zootopia. You cannot publish this per the assumed definition above.
Broadly speaking, Publish means releasing your story for the public to read and review. This is fine for both ventures. Fan fiction is not illegal to make/distribute under fair use guidelines. Since Disney owns all intellectual property rights to Zootopia, unless they specifically gives you permission, you may not use anything related to Zootopia (be it the titular city, that the characters you created are taking rookie training courses from Judy Hopps, or that your OC has a massive crush on Flash from the DMV) and make a profit off of it (and Mickey has powerful lawyers). If you aren't writing this to make money, but because you like telling a story, fear not, fan fiction generally falls in the catagory of fair use when it isn't making profit off of the copyright/trademark holder's own works and is transformitive in nature (adding new characters or building on the story premise are transformative).