I can see 6 other wires along with the white and orange wires coming into my house. These 6 other wires are connected to pins 1,3,4 and 6 respectively.
If I remove them, will they improve my broadband? Or do they have any affect when they are connected to the pins in my socket?
You only need 2 & 5. 3 was the ring wire & the others are connected just for neatness, they don't go anywhere.
Disconnecting the ring wire back in the early days of ADSL could improve a connection, I've no idea if that still applies to VDSL. No benefit that I know of in disconnecting the others.
If these are wires in the external cable coming in to the property, they will perform no function and should not have been connected to anything. Are you sure they are wires from the same cable as the orange and white? What colour are the wires?
Possibly, but unlikely to have any effect on your broadband.