David Tennant isn't doing series five, Matt Smith is taking over as the eleventh Doctor at the end of the year, his companion is Amy Pond played by Karen Gillan and Steven Moffat is taking over from Russell T Davies, so it will most likely be totally new characters of his creation from now on. If you mean clone Doctor and Rose then I doubt they will have 10.5 in the new series because it would over shadow Matt.
Billie Piper does have a small role/cameo in one of David's final episodes though, but it will be Rose before she met the Doctor so she will have no idea who he is.
No there isn't.
No she was not in series 5.
I don't think so. After the human version of the doctor went with Rose Tyler to the parallel universe, they don't appear again in the program. Both actors (David Tennant and Billie Piper) do appear in later series (in the 50-year anniversary), but not in this specific role.
BilliePiper
Her mum is Jackie Tyler, who is played by Camille Coduri.
When Rose first meets The Doctor it is stated that she is 19 years of age.
New Earth (series 2 episode 1).
David Tennant has a daughter, Olive, born in March 2011, and he has adopted his wife's son Tyler in September 2011.
Rose Tyler and David Tennant (as the Human Doctor) will both be returning for the Doctor who 50th Anniversary Special in 2013.Martha Jones has not been confirmed as a returning character.
Rose Tyler, not Rose Martin, was portrayed by actress Billie Piper in the long-running British sci-fi series "Doctor Who." She first appeared in the show's revival in 2005 and became a companion to the Ninth Doctor, played by Christopher Eccleston, and later the Tenth Doctor, portrayed by David Tennant. Piper's performance was widely acclaimed, and Rose Tyler remains one of the most beloved companions in the series' history.
"Doomsday" is the final episode of series 2 of the revived Doctor Who series (2005). It features the departure of companion Rose Tyler and the first appearance of the Daleks and Cybermen in the new series.
Tyler David goes by Ty.