OK a three parter question.
1. Offgassing windows. Yes windows can offgas depending on materials used, what was used to install it, etc... Though in many cases by the time a window gets to be installed it is done offgassing.
2. Removing bathroom caulk. As for the caulking itself, generally no safety issue but I would recommend a respirator in case of mold.
3. New furniture. Now that one is tough to answer as it varies based on materials, how closed up the space is, etc. One of the most effective ways of eliminating off-gassing or lingering smells is to let the areas breathe, open windows, and use an ERV/HRV.
For more information:
Read "The gap between my tub and tile needs to be re-caulked, but the caulking I found warned of cancer. Is there a safe, green alternative?" a Q&A answered by Randy Potter.
Also, check out this blog post Sean made on his company site. While this was written mainly for remodelers, it may help you learn some tricks to help air the place out.