To answer the first part of your question, there's almost nothing (solid) except a few types
of plastic that can't be baked inside polymer clay and usually on it too.
There may be a few pigments that could change color a bit with even the very low heat used to cure polymer clay though, and some plastics can shrink or even melt (polymer clay is a plastic too, but the kind that only softens a bit when heated).
polymer clay though must be thoroughly dry, including twigs, etc, since any moisture will turn to steam and swell and get trapped inside polymer clay (since it's oil-based, not water-based). That can cause bubbling or areas of opacity in any clays that have translucent in them (more than you'd think)--often called "plaquing" or "mooning."
Porous materials and very slick materials may not stick easily to raw polymer clay unless the clay is just pressed straight on and/or wrapped around, so often permanent white glue will be painted onto those surfaces first then allowed to dry before the clay is added. Sometimes there will be a little moisture left in the glue but doesn't seem to matter because it itself is kind of trapped in the (plastic) glue and the glue will act as a buffer too.
You can also mix more particulate materials into polymer clay (often into translucent or tinted translucent clays)... those would be called inclusions and are sometimes used to create "fauxs" too.
Paints and other colorants are also mixed into polymer clay sometimes, or laid between layers of it, etc. Again, the problem of water-based colorants comes into play though.
You might want to check out these pages at my polymer clay "encyclopedia" site for more on how to cover various materials with polymer clay, use inlays and onlays, mix media, use other materials as permanent armatures inside the clay, use inclusions and colorants, etc:http://glassattic.com/polymer/covering.htmhttp://glassattic.com/polymer/pens.htmhttp://glassattic.com/polymer/eggs.htmhttp://glassattic.com/polymer/BOH.htm
(small bottles) http://glassattic.com/polymer/armatures-perm.htm http://glassattic.com/polymer/mixing_media.htmhttp://glassattic.com/polymer/onlay.htmhttp://glassattic.com/polymer/mosaics_inlay.htmhttp://glassattic.com/polymer/inclusions.htmhttp://glassattic.com/polymer/Faux--many.htm
(also separate pages for faux wood, ivory, and turquoise)http://glassattic.com/polymer/color.htmhttp://glassattic.com/polymer/paints.htm
--especially (artsits') oil paintshttp://glassattic.com/polymer/letters_inks.htm
> Alcohol Inks
There will be discussions of "covering" other items with polymer clay in some kind of way on different pages at the site too (book covers/cardstock/notepads/etc, frames, rocks, inside sculpts, etc.):http://glassattic.com/polymer/contents.htm
As for the second part of your question, not sure I understand it:
Also, I have heard that some people glue things on before baking them, such as wood. Would this cause harmful fumes from the glue? Of course being baked after its already dried for a day.
Do you mean gluing wood things onto polymer clay before baking them both together, and after the glue has dried a whole day? If so, those wood bits would be "onlays" and they can be put on the clay in various ways:
...pressed into the raw clay
...glued onto the baked clay
...impressed into the raw clay and removed, then glued back into that impression in the baked clay
Some glues wouldn't be great to bake, especially petroleum-solvent-based ones, but permanent white glues are fine (Elmers GlueAll, or stronger brands), and liquid polymer clay is an excellent glue for polymer clay (though not tacky, and must be heat set).
Those that would be okay don't need to dry a whole day though.
If that's what you meant, you might also want to check out the Glues page at my site (as well as the Onlays and Inlays pages):http://glassattic.com/polymer/glues-Diluent.htm