Note there are now two versions of the App, original DJI Go is what you need for Phantom 3.
There's a new one called DJI Go4 which is for the latest models like Mavic, Inspire2 and P4Pro.
Having said that it might still connect to older range, but over time they will diverge more and more.
You can have both on the same device if you run two or more of different vintages - but makes ure the one not in use is fully closed down.

So far as I know none of the firmware updates can be forced.
My P3 hasn't been updated since late 2015 but I'm also running an older app with it so not sure what happens if you can only find a later version.
The device it runs on is a Nexus 7 and it goes on wifi to cache maps and is on latest Android version available to it.

Generally you want to either stick with what works well for you now or update to all latest. 
I don't know much about Apple but in google play you can check a box to not auto update on the app page.