That would be "Det här är hans te."
"Det är hans te." (It's his tea.)
"Nej, det här är hans te." (No, this is his tea.)
I am assuming that often "det är" would merge together in spoken swedish and sound more like "dayr" correct?
Yes, although the exact sound will differ depending on the region. In my Stockholm Swedish it becomes more like /deː/ (as "är" itself is commonly pronounced /eː/ in everyday language by many Swedes, unless you're being intentionally clear and articulate). Deehanste. :)
More or less. It will often fuse together to /de: e:/, without the silent R of är.
Too confuse you further, sometimes "är" is just pronounced as "e", as rhblake above writes, but the first word is still whole:
"de e hans te"
I meant how do you tell the difference when speaking? How are the pronunciations different? I know what they mean. :)
Oh, okay, I couldn't tell from your question what you meant. The audio and pronunciation is pretty distinct for both of them: hans is pronounces like the english huns, or the genitive form of Han (as in Han Solo). The first sylable of fenes on the other hand is more like the english word hen (as in the female chicken) and the es also carries the same e sound. As you see, the A and the E in swedish have their own distinct sound. It's kinda hard to explain how things sound in a certain language, it's probably best if you either listen to the adios Duolingo provides or to the ones on Google Translator.
"Sitt" specifically means something belongs to the subject. I don't know what the exact rule for when to use which, but it can help avoid confusion about who exactly something belongs to. To give an example, "Han älskar sitt husdjur" always means "He loves his pet", his own pet. "Han älskar hans husdjur" on the other hand means "He loves his pet" in the sense that he loves a pet belonging to another male person.