Yes
Yes.
If you are talking about Shrewsbury in England, then as both are in England you will not need a passport to travel there.
For a Greek citizen: identity card or passport.
Yes, you will need a passport at each end of the journey.
Yes.
No
You will not require a passport to travel from Sunderland, England to Falkirk, Scotland.
yes dumbo
Yes, you need a passport to travel from England to anywhere outside the EU. You may need a passport, or other acceptable ID for countries in the EU.
only if you are going to Northern Ireland, you need a passport to travel between England and Ireland.
I have danish authority convention refugee passport and want to travel to England. Do I need visa to UK?
You only need a valid passport.