Sword, Tea and Turandot is not an action story. It is really a reconciliation of Jackie Tyler to the strange life her daughter and The Doctor live. The first part, with Jackie watching their sword fight is very much a rite of passage. Jackie finally realises that Rose has grown up in The Doctor’s care. The second part is an insight into Jackie’s world, and an example of The Doctor’s compassion for the put upon innocent everywhere. As well as a reference back to On The Western Front, when The Doctor and Rose met her great-grandparents in 1916. Pete Tyler’s mum is the wife of the son Michael Tyler and Nurse Rose Cotton who they met at the field hospital on the Somme, were destined to have.
As for the Turandot scene, again it was to bring Jackie into the fold as somebody who shares the wonder of knowing The Doctor and being able to do things that would be impossible otherwise. Turandot in Bejing was a perfect backdrop to the scene. The story of what happened at the first performance of Turandot, as related by Rose is true. Most Doctor Who fans already know that Puccini died with it unfinished, however, as it is mentioned in the 1996 movie. It is one of those things like how to spell Buffalo and how old Madame De Pompadour was when she died that Doctor Who fans will never forget.
And of course, this story is a set up for a future story when many apparently unimportant elements of this one are referenced.