Most of that connects pretty seamlessly without much hassle. Amazon's Echo controls Philips Hue lights directly through the Alexa app, and Nest links up easy from there too, so technically you can run everything from a single app no problem.
What you will notice is that some of Nest's more advanced features (like super specific routines or complex automations) sometimes it's more convenient to set them up from the Google Home app, because Nest is Google's. But for everyday stuff - turning lights on, lowering the temperature, that kind of thing - it all works perfectly integrated into Alexa without having to jump between apps.