It's worth noting that other browsers' "private browsing" modes only hide the details of the session from the local machine. Using "incognito mode" in Google Chrome is not encryption and does not shield your privacy in any way from others on your network, your ISP, the NSA or Google themselves.
Check out a documentary called "The Lightbulb Conspiracy" on planned obsolescence. They find a Canon or Epson printer with a chip inside that counts the number of prints made, and after some arbitrary number will throw an unrecoverable error essentially telling you it's time to buy a new printer. By the end of the movie, they've reset the chip without any hardware modifications and the printer continues printing just fine.
In most states, you can be detained for up to 72 hours while charges are being filed against you, but if they can't charge you with a crime in that time, you're free to go. Be aware that in general interactions, officers will try and make it seem like you're not allowed to leave, but just ask if you're "free to go" and they'll have to either let you go, or figure out a real reason not to.
No, they can't require you to divulge a password. However, if your "password safe" is anything less than completely secure, they can legally spend as long as they need cracking it and get what they want using a warrant.
It's a shame. If people could refuse to work on moral grounds, we could stop the blind pursuit of money from powering the largest organizations on the planet (instead of the moral will of any actual human, be they worker or executive).
Incognito mode is not encryption and cannot prevent people on your network, your ISP, the NSA or Google themselves from keeping an eye on your data. The effects of incognito mode are specific to the Chrome browser on that machine (and the cloud backup you may allow Google to keep of this data, such as if you log into Chrome).