If you only pay for a Broadband service and not landline telephone service, can you still make emergency calls (999) from a corded phone plugged into the landline?
Yes. The landline will still be working. If you don't have a calls package you will be billed on a pay as you go basis for normal calls, 999 calls are free.
If you have a broadband package from BT then that include landline rental bt as @gg30340 posted you are charged for any calls but emergency calls to 999 are free
Depends, when you say you only have Broadband do you mean you have a SOGEA, aka Naked DSL Line? If so I believe you can only make calls via the Digital Voice Service.