In British English "opposite from" (particularly when talking about the location of something, e.g. buildings, offices, shops, etc.), is perfectly normal, but is not accepted here. In normal speech one would almost never say "my house is opposite to the school".
(not immediately relevant but worth remembering : One could also use "opposite of" when talking about opposing points of view, e.g. "my view is the opposite of yours").
Interestingly czech and slovak prepositions take precisely the same cases as polish. I assume there is some protoslavic root for that. If i tried to find rules i would say that direction takes accusative generally. Why w is accusative for weekdays but locative for months remains a riddle.but that same rule is also valid for polish as well as czech and slovak.
Here is a useful table. As you can see, some prepositions take two different cases, depending on their meaning: https://www.polskinawynos.com/wp-content/uploads/2018/04/przyimkiprzypadki.pdf
Well, I think that only makes sense when the players are standing on their halves waiting for the referee to start the game - theferore, they are literally standing vis-à-vis each other.
I'd say that the most common ways to denote what you mean are:
"kontra" (contra, versus): simply "Liverpool kontra Chelsea". But as both use Nominative, it can be used in limited contexts only, like: "Dzisiejszy mecz to Liverpool kontra Chelsea". For example, "Dziś wieczorem Liverpool kontra Chelsea" doesn't make grammatical sense, although if you added a colon after "wieczorem" it could be treated as a title, and thus it would be ok.
"przeciw"/"przeciwko" (against), needing Dative for the second team: so it's still "Liverpool przeciw(ko) Chelsea", but "Chelsea przeciwk(ko) Liverpoolowi". No problems with using in sentences, like "W dzisiejszym meczu Chelsea zagra przeciwko Liverpoolowi".
"z" (simply "with"). Needs Instrumental, unsurprisingly. "Dziś wieczorem Chelsea zagra z Liverpoolem". (Tonight Chelsea will play with Liverpool).
Actually, as "Chelsea" is treated as a feminine name not ending with -a (it does, but not in pronunciation), it will be the same for every case. "Liverpool" is masculine, so it undergoes declension.