Yes to both questions.
You will need to make sure that the channel used by the
Sky + box to send the signal out is the same as your old Digibox. Ask the installer to check this and change if necessary.
If you put the old Digibox in the bedroom then you obviously need a a cable from the satellite dish. You'll probably get a 4 output LNB (a Quad) fitted to your dish for the
Sky + which needs two of those outputs. You
MAY be able to persuade the installer to run an extra cable for you if you cross his palm with silver.