Thtat definitely looks like you have a corrupted image somewhere.
If you have the "continuously busy 'processing'" at start-up, then probably some recently imported image is corrupted.
What I usually do to track down the culprit is to defer the generation of previews on start-up:
Press the Shift key immediately after you start Aperture to prevent preview generation for that session. This should take care of the "processing". Then systematically select some of your most recently imported images and try to update the Previews for them (Aperture menu bar -> Photos-> Update Previews). If Aperture stalls/crashes again, then you will know that the culprit is among the most recently selected images.
Inspect these images careful in the inspector (launch Aperture again with the shift key held down) and look if any one of these look suspicious (file format, size, filename or version name). E.g. I once managed to crash Apertue by importing a 2GB file, or b importing a file with invisible characters in the filename.
Remove the suspicous files and see if this solves the problem.
If you have the photo stream turned on don't forget to check the PhotoStream or your MobileMe albums for corrupted images.
To answer your question:
If not, how do I save parts of the library and bring them back later after finding they are OK?
One way to do this would be to export Aperture items (albums, projects) as a new library (File -> export -> Project/album / as new library. This will preserve all edits, keywords, tags, folders, etc.
Later you can reimport this library and merge it with your current library. (File -> Import -> Librar/Project)
Regards
Léonie