Google Nexus 6 Apps Crash and Random Restarts

Hello everyone! I'm posting this because my Google Nexus 6 phone has been giving me some serious problems. To start off with, this phone is new (purchased about 1 month ago). Since I first got it, I have been receiving little error pop ups saying "Chrome has stopped" (among essentially every other single app doing the same thing). My phone also randomly will restart while I am using the phone. This doesn't appear to be based on the battery charge, as it has done this when my battery has been low (15%) and high (90%).

These problems have been annoying, but so far I have put up with them because I am still able to use my phone. The latest to happen, though, is that I receive, on start up, this message: "Google has stopped". The effects of this are that I am unable to access my home screen at all (only my wallpaper is visible) and I am only able to get to apps that I already had open or get the the settings via the pull down menu.

What I'm wondering is: is there a solution to this, other than tossing it into the trash (which is tempting)?

I'd appreciate any advice or thoughts I can get on this! Thanks for reading :)