"Where are the desks?"
I believe you are definitely right. A desk is письменный стол or парта. I have reported.
That seems to be more specifically a "writing desk", but I would think you might try to report it and see if it might also be allowed. http://dictionary.reverso.net/english-russian/desk
They are completely different. Ь is a soft sign, it changes the previous consonant by making it soft (palatised). See my answer here for some examples.
Ы is a vowel. English doesn't have this vowel, it's something in-between u and i. In fact, Ы is completely unrelated to Ь: in the past, it was written ъі, so it's related to Ъ and not to Ь (but the relation to ъ is not obvious in modern Russian either).
If you're familiar with the international phonetic alphabet, ы is pronounced [ɨ] while ь palatalizes the preceding consonant (e.g. ть will be pronounced [tʲ]).
Why are some plurals formed with и and some with ы? Is it for masculine and feminine or the other way around? And am I right in generally assuming that the nouns finished by "o" are masculine and with "a" feminine?
No, it depends on the last consonant of the stem.
For example, in «стол», the last consonant is hard, so we use «ы»: «столы́». In «ко́нь» 'horse', the last consonant is soft (нь), so we use «и»: «ко́ни».
Some consonants don't have a soft/hard distinction. They always use «и». E.g. мяч 'ball' — мячи 'balls,' нож 'knife' — ножи. For historical reasons, к, г, х fall into this group: каза́х 'Kazahk' — каза́хи. Even though they technically have a soft/hard distinction in modern Russian, the ending is still -и.
It's the same for feminine nouns. Липа 'linden' has a stem лип-, it ends in hard consonant so the plural is липы. Ба́ня 'bath house' has a stem бань-, so the plural is ба́ни. Да́ча 'dacha' has a stem дач-, ч doesn't have soft hard/distinction, so the plural is да́чи.
There is no way to distinguish masculine and feminine nouns in plural.
In my opinion: Где письменные столы (without находятся) should also be correct
Why does the pronunciation of the vowel "о" change so much between стол, столе and столы?
In сто́л, O is stressed so it's pronounced like O.
In столе́ and столы́, O is not stressed, so it's pronounced as a reduced vowel closer to A than to O.
«Стол» is singular, «столы́» is plural. (Both are Nominative case forms.)
Prepositional is used after prepositions. We don't have a preposition here.
If you reworded a sentence with a preposition, you'd have a prepositional case: В како́м ме́сте столы́? 'In what place are the tables?'. Here, «како́м ме́сте» is prepositional.
Is there a difference between desk and tables or are they being mushed into the four legged things that stub your toes group?
Can anyone please tell me the difference between " стол" , "столы" and "столе"
Стол - one desk Столы - many desks, plural noun Столе - Prepositional case of стол (http://www.russianlessons.net/grammar/nouns_prepositional.php)