It's like "a" and "an" in English. If it gets too hard to pronounce a wild 'e' appears.
The rules are not so easy as in English tho. Basically if the noun begins with "w" or "f" followed by yet another consonant, there will be 'we' before. So for example:
we wtorek (on Tuesday)
we Francji (in France)
we Wrocławiu (in Wrocław)
w wojsku (in army)
w Finlandii (in Finland)
It also works with the word 'mnie' (me):
- We mnie (in me)
In other cases, when the word begins with at least two consonants both options are allowed:
We śnie* / w śnie (in a dream)
We mgle* / w mgle (in a fog)
We Środę / w Środę* (on Wednesday)
We Czwartek / w Czwartek* (on Thursday)
I marked the one that seems more natural to me with *, but as I said both are OK.
In the 'puzzle' exercise, you are expected to put the exact 'best answer', that's what the capitalization is based on. If you are able to create another acceptable answer (not caring about capitalization), then of course it's accepted as well. That's how the application works.
Sometimes I have a problem creating the English sentence from puzzles because there are other answers that seem more natural to me but I cannot build them...
Why when we say something is happening in a Month, we use a locative case... ie - "Styczen" becomes "Styczniu", but if we say something is happening on Tuesday, we don't change the case?
W styczniu (loc) on robi obiad
W sroda (nom) on robi obiad
Is it because 'w' translates to "in" when talking about a month, but translates to "on" when talking about a day?
We do change the case in both situations. As you wrote, "W styczniu" takes Locative, but it's not "W środa". It's "W środę". Which is Accusative. Now, why does it take Accusative and not Locative, I have no clue... but it does.
"We wtorek" is also Accusative, but it's grammatically masculine (and inanimate), so Accusative is identical to Nominative. But the three feminine days (środa/sobota/niedziela) easily show the difference.
There are many tricks in Polish but they always make sense in the end. But here I just can't find any sense. What is the rule here, it depends on the noun itself despite "w" meaning the exact same thing? It takes accusative when it's a day of the week but locative when it's a month? What about a country, a season of the year, a building, a planet...?
My "dinner" which I put by mistake was accepted as a right answer, should it be that way? In earlier lessons we were taught that obiad is lunch and kolacja is dinner, obiad=dinner was unacceptable there. Yes, I know obiad and dinner are both the main meal of the day and historically had been the same before dinner eventually moved from afternoon to evening, so the matter isn't that straight, but would it be more logical to keep the terms consistent throughout the course?