Do you need permission to take out a chimney breast in a terraced property?

No

Yes if house is a listed building, yes if chimney breast is on a party wall if house is not at the end of the terrace as the party wall act comes into play. At the very least you would require building control input and approval so they would have to be notified.

Yes ask your Mother and Father before you do it and make sure your homework is done first !!

No. It is a permitted developemnt. But you need to inform Building control and do a party wall agreement.

You don't need planning permission but you would need to get a structural engineer to provide you with the calculations on what support you would need to put in because it's a load bearing wall then once the works been done you'd get building control in to make sure the jobs been done properly and sign it off.