I'm not sure I know why the weather app crashes but I would start by uninstalling, re-downloading and reinstalling.
I have never had good luck syncing my Facebook contacts with my phone contacts. You can manage the sync settings for your Facebook account in Settings/Accounts & sync. Personally, I like the free app SyncMyPix which lets you sync your contact's Facebook profile pictures to your contacts already in your phone. With this done, you should be able to see your Facebook contacts in the People application which I believe replaced the Contacts app in ICS.