a 3g / 4g capable device to connect to your laptop (USB or similar), or a laptop with built-in 3g / 4g card.
No, you don't.
Look up MiFi.
I contacted BT and asked for a broadband phone line.
Friends don't let friends touch BT broadband with a bargepole.
Avoid doing direct business with any aspect of BT Retail (and indirectly via Wholesale/Openreach as far as feasibly possible by using LLU broadband etc. ).