"Seth has a scarf and a t-shirt."
Translation:عِنْد سيث وِشاح وَتي شيرْت.
Because this is in MSA, modern standard Arabic, not dialect. Arabic is a VSO, verb subject object, language ;therefore عند need to be first.
I might be wrong but in Lebanon, I'm used to say for example سيث عِنْد and not the other way around, I would like to know if it's just a mistake.
You're right, you wouldn't hear it used like this in a real world, always like you said - Seth 3ando (...). This is Fus7a though, so formally this is correct.
Dialect is a bit different from fus7a. In algerian/lebanon dialect, I would normally say seth 3ando, but in fus7a, you must say 3and Seth, because fus7a arabic is VSO (verb-subject-object).