so when they both died in battle, harry (as godfather) should have brought up teddy (or tommy) but in the nineteen years later it refers to teddy in a different way :
"snogging victoire (who i guess may be bill and fleurs daughter or something?)
and they said he comes to dinner 4 times a week and then harry says "why dont we invite him to live with us"
so teddy is not living with them and who is looking after him?!
His grandmother, maybe?
I was going to say that!!
I'm not certain of Lupins parentage, but I can tell you that Nyphadora Tonks had a witch mother (she was blown off the Black Family Tree) and a Muggle Father Ted Tonks. Ted was killed by death eaters while on the run. So when Tonks gave birth the 'boy' was named after his Grandfather. Tonk's mother was left in charge of the baby when Lupin and Tonks came to Hogwarts to fight in the battle against the deatheaters. Thus leaving 'Teddy' with his Grandmother.
After all Harry had been through and being aged only 17 I doubt that he would have been expected to take the child and bring him up.
Neville was bought up by his Grandmother and I'd have suspected that he like Harry would have had a godparent too.
As for Teddy being werewolf, I'm pretty sure that JKR said at the birth he was displaying tendancies to having the same talents as his mother - he wasn't born as a cub!!
Plus, although Harry was asked to be his godfather he never actually went through with any sort of ceremony that would have made it official. But, well, do any of us really know whether or not the magical community celebrate a baby's birth with a Christening, as it is a Christian celebrationary tradition orgionally...right?
Ya Teddy was probally raised by his grandmother but Harry and Teddy probally visited each other often.