You need to update to 6.01 for the first bug. I suspect you need to do a full uninstall and reinstall first.
Reinstalling made the problem worse. It asks me to sign in to Adobe.com, and then nothing happens.
Is there a 6.0.1 download available somewhere? The only 6.0.1 upgrade instructions I've found tell you to launch 6.0.0 and then use the update feature within the app.
That is a really stupid way to release an application start-up bugfix... tell the user to start-up the app to apply the fix!
I've gone through this screen several times now. It comes up every time I try to start LR6. I go thru the sign-in, accept the agreement, and then nothing happens:
The download link to LR 6.0.1 is available at ProDesignTools. Make sure you do the important instructions to authorize the download from Adobe: http://prodesigntools.com/adobe-lightroom-6-cc-direct-download-links.html