What language does the Meta-Crisis Doctor speak in the parallel universe, considering he does not have the Tardis around him? How did he learn English?
The Doctor speaks English.
He's spent more than enough time in Britain without a TARDIS that he must be fluent in English. It's not surprising really: he's a 1000-year-old Time Lord who spends an awful lot of time on Earth and in Britain, and a good deal of his competence and awesomeness is based not just on fancy technology such as a universal translator but also on his own knowledge.
See also bitmask's excellent answer to Does The Doctor hear everyone speaking in Gallifreyan?
Plus, the Meta-Crisis Doctor is half-Donna.
The Meta-Crisis Doctor, created along with the Doctor-Donna from a single meta-crisis event, is part human, just as Donna becomes part Time Lord. Donna gains Time Lord knowledge from him, so it stands to reason that he should gain human knowledge from her. Even if we assume that the Doctor wasn't fluent in English (or perhaps that his English had grown rusty after so long relying on the TARDIS and its translator), the Meta-Crisis Doctor almost certainly would be, simply from being half-Donna. We even see him speaking in a more Donna-ish way than the usual Tenth Doctor:
DONNA: Oi, watch it, spaceman.
NEW DOCTOR: Oi, watch it, Earth girl. Ooo. I sound like you. I sound all, all sort of rough.
NEW DOCTOR: Oi!
NEW DOCTOR: Spanners. Shush. I must have picked up a bit of your voice, that's all. Is it? Did I? No. Oh, you are kidding me. No way. One heart. I've only got one heart. This body has got only one heart.
DONNA: What, like you're human?
NEW DOCTOR: Oh, that's disgusting.
NEW DOCTOR: Oi!
-- Series 4 Episode 13, Journey's End
Even if you assume that the Doctor couldn't speak English without the Tardis already, the metacrisis is part human. If the Doctor Donna gained enough of his intellect and knowledge to defeat the Daleks, it stands to reason that he could absorb enough of hers to learn her language. He does adopt a few of Donna's mannerisms.