On windows phone and windows 10 mobile, it is not natively possible to check the real download and upload speed of the network but an XDA developer user has churned out an app that displays this very information and more. Using this app, you will be monitor CPU + MEMORY (RAM) + GPU real-time usage; I/O real time usage and fetch list of every device and driver available within the phone.
The application is called the Device Portal and it is totally free to download from windows phone store. Other nifty features include ability to get a collection of every app installed (With settings and hidden) and find list of active system processes with CPU and RAM usage (Private Working Set). You would also be able to restart or shutdown windows phone without using hardware buttons.
Keep in mind that you will have to enable the app without authentication from Settings > Update & Security > For developers > Developer mode.