... Yes, of course, it's the "accurate" translation, but that's voluntarily blinding yourself from the fact that in 99,9% of the cases in English, if you want to be polite, you will just say, "Please" and that this word is best translated as "S'il-vous-plaît" or "S'il-te-plaît" in French. "Translation" doesn't mean actually taking all the words and putting them directly in the other language. It means transferring the words so that they will make the same sense in the target language. "If it pleases you" (because, yes, that's the correct translation) is extremely awkward, unnatural and uncommon English. However, "S'il-te-plaît" is as common, widely used and normal in French as "Please" in English.
Here's a little chuckle for you all: I was having trouble hearing the pronunciation, and guessed "Une pierre, s'il te plaît". ... After seeing the correct sentence, I now understand that a person is much more likely to ask for a beer than for a stone! Quite funny, in my mind.
In French, there are not countable/uncountable nouns as in English (but rather countable/uncountable quantities) In a bar:
"A beer" = "une bière" = it means a "glass of beer" usually when you're in a bar. You wouldn't order "un verre de bière", you just have to say "une bière!"
"A can of beer" = "une canette de bière" (you can order "Une bière en canette s'il vous plaît!" also for instance)
"A bottle of beer" = "une bouteille de bière" ("Une bière en bouteille s'il vous plaît!" is also possible)
Nothing make a word feminine or masculine, it's simply the way they are... Like they have accents or no accents, they are feminine or masculine. (The etymology sometimes explains why, here it probably comes from a Germanic old French, "bira" that is feminine. )
It's simply "une bière", "la bière", and if you remember for instance "la bière", you will always remember it's a feminine noun.