A web proxy can speed up your connection and reduce the amount of data being pulled down off of the internet. There are some caveats…
First off space is a limiting factor, the Mikrotik can only store so much before it starts getting overwritten.
Second proxies will only cache data after the initial connection. Thus only subsequent connections to the same page will see any benefit if the proxy serves up the content locally that hasn’t changed.
Depends on how you setup your proxy and what the app is “talking” to. If the app is simply “calling” a web page, then yes it should work. If the app is accessing other data, then you will have to ensure that the traffic for the app goes through the proxy.