You are asking about essere versus stare. Both usually (but not always) translate as "to be". Two problems: the English verb carries several meanings, and Italian usage varies regionally. Here follows a translated explanation from the Accademia della Crusca - the official guardians of Italian.
The verb stare is often used instead of the verb essere, especially in phrases that express a person's behaviour or state of mind: Stare attento "To be careful", Stare in ansia "To be anxious", Stare sulle spine "To be on your toes", or in phrases that contain an order or an exhortation: Stia zitto! "Be quiet!", Sta’ seduto "Be seated!", or in fixed phrases: Se le cose stanno così... "If things are like this..." In these cases the use of stare in place of essere is legitimate and correct; in other cases the two verbs are not interchangeable: you can't say or write Sto nervoso "I'm nervous", Sta assente "I'm absent", Il lavoro sta fatto bene "The work is done well". The habit of substituting stare for essere is of southern origin; this strong regional character must be avoided in official and formal uses. With family and friends, instead, you can stay (stare) more relaxed.
The following considerations are valid for the national language, not for regional Italian (in which variable uses apply).
In the sense of "being in a given place", referring to objects, there is a nuance between the two verbs: essere expresses the location with reference to the moment of enunciation, while stare denotes the usual location; compare these two sentences:
(1) The scissors are (sono) in the first drawer to the right of the sink [where they are now, not necessarily always]. (2) The scissors are (stanno) in the drawer to the right of the sink [where they are normally placed]. NB. THIS IS DUO'S USAGE HERE.
Referring to people, the verb stare, in modern neutral use - different, in part, from past uses - generally has the sense of "staying", "residing", or indicates the posture, or, of course, the state of health. Then there are idiomatic expressions, unalterable.
For example these two sentences have a slightly different meaning: Sono contento di essere qui = "I'm happy to be here [at this precise moment]"; Sono contento di stare qui = "I'm happy to be here [always]". The first sentence expresses the place in space and time; in the second, it emphasizes instead permanence in the place of which we speak (so that, invited to dinner at a friend's house, I would always use the first: the second could be misinterpreted by some touchy soul).
The relations between the two verbs are complex, and not always clear, also because of regional differences. But phrases like Dove stai? (in the sense of "Where are you?") or Non ci sta nessuno (for "No one is present") are not acceptable in supra-regional Italian.
Thanks for that detailed explanation. I came to Italian after speaking Spanish pretty well, and Spanish uses its verb related to stare (estar) for many more uses. I had just decided that Italian didn't use stare for location or position, a major use of estar, when I encountered this. I haven't "digested" it all yet, but it is quite helpful.
They both have many meanings, varying with context. For su, there are loads of examples at https://www.thoughtco.com/italian-preposition-su-2011462. For sopra, there's an explanation at https://www.thoughtco.com/italian-improper-prepositions-2011436. Note especially that it gives "on top of, upon, above, over" but NOT "ON". It's a good guide: sopra is about superposition, not contact. I think Duo would be better off with "upon" here.
A huge list of examples is in the Italian-only dictionary at https://dizionari.repubblica.it/Italiano/S/sopra.html, and from there you can also get to the Italian-English version.
That's not grammatical, or rather it is but "lamp stand" is a noun phrase meaning Il lampadario (la basa della lampada).
If you actually typed "stands", possibly yes, but si trova is normal for that meaning. Stare here means "to be" (in a place or situation).
But why not try "stands", with the spelling corrected, and let us know.