>>> Can Echo control devices outside of its home network?
Absolutely! I have done it already. Your Alexa app is tied to your Amazon user account, so there is no security risk, either. No one can get onto your Amazon Echo account unless they have an Alexa app containing your Amazon account name and password (as my wife does). Best of all, you can test this with your current Echo, so no need to be in a car to test, either.
What I did was shortly after getting the Echo, I was walking to our neighborhood mailboxes when I thought I would use Alexa app to have Echo turn on and play a TuneIn radio station in my Alexa list of Favorites and startle my wife who was in living room reading the paper or something. Being a Comcast customer, I connected my phone Wi-Fi to the free xfinitywifi signal Comcast customers can use; xfinititywifi is all throughout my neighborhood. I turned on Alexa app and turned on Echo before getting back in the house. The Echo was playing the radio, and my wife was completely baffled and startled by what had just happened. I told her how it happened. Turning YuneIn off was not possible without asking Alexa to turn it off, but the app enabled me to pause the radio which accomplished the same thing.
So, try this at home. Connect your present Echo to another Wi-Fi signal as I did, or tether it to your phone's hotspot or data plan. Now, your Echo is on a different network, and tell Alexa via app to do something while you are standing next to it. It will do it. Undoing actions is not as easy (like turning off TuneIn through the app), so I need to put in a suggestion to Amazon that there be a way through the app to tell Alexa, STOP.)
So, give this a try and experiment with what you can and cannot do this way.
If you like this Echo idea, you will probably like this one:
Within the past few days, at the WD User Forum which I am a member of, I posted complete instructions on how to easily make your own homemade "wireless drive" that can be used (for example,) in car and elsewhere to stream videos to the kids' tablets when they are in the back seat!
I actually have a WD wireless drive, but this is a way to make one if you don't have one.
Here is the link to that post (Just like here, you don't need to be a forum member to read the posts.):
https://community.wd.com/t/easily-make-your-own-wireless-drive/154596Have fun!