Yes it will. But i would recommend using an ethernet cable than wifi where possible.
You may find where the usb gets too hot and the wifi stops, you should unplug it and let it cool down before using it.
Ethernet is running an ethernet cable directly from a device such as a pc to the router/modem which allows internet access. The cable is preferred because you always have access to internet until you unplug the ethernet cable or the internet cuts out.
Wifi transmit radio signals at a certain frequency range. You need a wifi router and wifi adapters or wifi compatible devices. The wifi adapter can convert those radio signal into electrical signals and you have access to internet. Whilst it is wireless, it is not a sustained signal. there can be object which reduce the strength of the signal hence your internet slows or cuts out for a few seconds.
This is a good video at visual explaining as well: https://www.youtube.com/watch?v=Sue1Zvmh8JA
So if I buy the part I showed you, will I be set to connect to the box, its a fibre optic broadband with a green glowing light at wifi,
Yes it will work since it is a wifi router. You also have a wifi password stated on the router by a sticker which you will need. It will also have a name, make sure you know which wifi network is yours.