You probably heard the fast-speech version of the word, read like "soln". It's quite common in casual speech to drop the unstressed e in this environment. Generally I've heard the e dropped in words ending in -len, -ren, and even -nen (for example, my brother-in-law pronounces "Kolonnen" like "Kolonn" in fast speech). The z-sound at the beginning is instead a standard feature of Hochdeutsch (standard German): a single s is always (also at the beginning of a word) pronounced like English z, a double ss or the letter ß are always pronounced like the c in price instead. Some regional German variants, however, do have a "strong" (unvoiced) s-sound at the beginning of words.
At normal speed, I hear "Wohin sollen die Getränke?" At the slower speed it's "Wohin zung die Getränke?" I generally find the slower speed separates the words, which may be run together at normal speed, but except for sometimes being run together, the words are more accurately pronounced at normal speed.
I don't believe the preterite form is used very often, since it's identical to the subjunctive form which is common. But the meaning would be similar to what past tense always does: "was obligated to [do something]." You could also maybe say "should have" or "ought to have," though the preterite "sollten" wouldn't as much imply that you didn't actually do the thing.
"Sollen" or "wollen," depending on whether you're talking about being obliged or needing to do something, or just making a factual statement about the future.
"Sollen" can more or less translate to either "shall" or "should." However, Duo teaches American English, where "shall" is not used commonly, so Duo might not consistently accept "shall."
As I said, Duo is geared toward US English, and here we generally say "should" where you evidently use "shall." The issue here is just a difference in US and British dialect. I believe "shall" is a perfectly good translation in your dialect; you'll just have to bear in mind that Duo's US-based usage is a little different.