"There in the box are gifts" has a slightly different meaning in English. The phrasing "there are" indicates the existence of something. But with "There in the box are gifts", "there" is acting as an indicator to "in the box". Because you separated "there" and "are", you're not talking about the existence of something being "in the box".
I think the sound of в is dependent on the consonant before or after. I probably read about it in some grammar book, but the point is it would depend on if the consonant before/after is voiced or unvoiced. If it's voiced, then в would sound like English "v"; if it's unvoiced, then в would sound like English "f".
Here, в sounds like "f" because к is unvoiced.
Edit: I looked it up. In chapter one "The Sounds of Russian" under "The Consonants", then "Voicing Rules" of Schaum's Outline of Russian Grammar (2nd Edition), it says "A voiced consonant is pronounced voiceless when followed by a voiceless consonant". The example is в театр - в sounds like "f". (Note however that в "does not cause a preceding voiceless consonant to be pronounced voiced". Твой is pronounced "tvoy", not "dvoy".
voiced vs voiceless is a real thing. The consonants in each pair have the same tongue position and the only difference is whether the vocal chords are engaged or not. In fact it is impossible to say D without using the vocal chords. Here are the paired consonants in English:
t vs d
f vs v
p vs b
ch vs j
k vs g
s vs z
sh vs the g sound in beige
th (in think) vs th (in that)
I think this depends on the particular language. In Italian, it is totally possible to say D without using vocal chords, and T/th with or without voicing: the difference consists, I guess, in the tongue being pulled backwards to pronounce D in contrast whith the T, where the tongue is pushed anteriorly and inferiorly. But the intriguing fact is that I clearly perceive the sound D in day, darling etc in English to be the same as in Italian. The only clearly voiced B I hear is the one pronounced by the male voice in DUO, when the vibrating sound even precedes the sound V, in a way almost caricatural ("uhmV")