Where was Fate staying during the first season? The DVDs I own of Magical Girl Lyrical Nanoha seemed to use very bad fan subs as when Alph first appeared, Arisa kept referring to her as a 'he' (despite clearly seeing her boobs), then Fate was named Feid, and Alph was Elofy.

In episode 7, Is This a Third Magician? (titled in the subs as The Third Magical Girl), there is a subtitle indicating where Fate was living. However, I don't trust it as shortly after when Nanoha gets off the bus to walk home and meets Yuuno with the repaired Raising Heart, there is a subtitle of where she is and not only is it totally different to what was shown with Fate's location, but it doesn't even says Uminari City which is where the the Takamachi's, Bannings' and Tsukimura's live and where Midori-ya and Seishou Elementary School located (as such it's very unlikely Nanoha was dropped off in another city after school to go home or to visit Arisa or Suzuka).

So I am wondering where was that apartment tower Fate was living in?
On Earth, Fate and Arf live in an apartment which is probably located somewhere in Uminari City. Apart from that, their home is the Garden of Time, the base of Precia Testarossa in the dimensional space.