I have what looks like almost the exact same design of dizi, with the red bands and ivoroid ends, but no brass joint. Mine is smaller, pitched in G (Western D). A friend picked it up in China.
Yes, it is played horizontally, as a transverse flute.
The description says it comes with a pack of dimo membranes, so you should be set for a while. The packs contain 5 membranes that you can cut up into right-sized pieces.
You'll need some dizi glue to attach the membrane over the dimo hole. If you don't have mule-glue (!), you can try cutting a clove of garlic in half, and rub on the sticky garlic juice as glue. Getting the membrane wrinkles just right is a fine art, so expect to experiment a bit. Or you can just tape over the dimo hole (like me) and play it as a regular flute, but without the buzzy dizi sound.
Keep in mind that the pitch of Asian flutes like this is designated according to what we consider the G fingering xxxooo, not the D fingering xxxxxx. So this C dizi is pitched like a Western G instrument. That is, the note that sounds when you finger xxxxxx is G, and we would call it a G flute.
As for the actual pitch and size ... I'm guessing this dizi is the equivalent of a low G (alto G) whistle, range G4-G6. Which would make the total length around 28 inches, sounding length around 15 inches. Dizi hole spacing is fairly tight, so that stretch would still be pretty comfortable. The Amazon customer comments suggest that the stretch is not a problem, by the absence of complaints.
The description actually gives the range as G3-A5, but I'm guessing that's a mistake. G3 is an octave below
a low G whistle. Which would make the sounding length around 30 inches and the total length around 48 inches!
I guess that's possible, but I doubt it. You'd need monster-sized hands to play it, and the flute could double as a nice broomstick. Maybe you can let us know when it finally arrives.
Good luck, and enjoy.