I have found out that please will be in Ukrainian будь ласка. In terms of Russian, it looks like singular. Is there any plural form for this word?
If I get the question right, you need two types of addressing people. One is for one person you need something from, another is for multiple people or for ones you address with respectful 'you'.
If you want to address one person, whom you usually address with singular 'you' (ти):
Будь ласка, допоможи мені.
Also: Будь твоя ('your' singular) ласка, допоможи мені. — very rare in use but indicates the type of 'you' better.
If you want to address multiple people or one person, whom you usually address with
respectful 'you' (ви):
Будь ласка, допоможіть мені.
Будьте ласкаві, допоможіть мені.
Also: Будь ваша ('your' respectful/plural) ласка, допоможіть мені. — very rare in use but indicates the type of 'you' better.
It is not a plural form of будь ласка, it is rather a way to use this expression for plural addressees or for those addressees you have too much respect to to say singular 'you' in Ukrainian.
Here's an interesting article about T-V distinction. The Russian-Ukrainian section isn't as precise as it could be but still interesting to read if you are out of context.
It's not a one word; it's two words. So grammatical category of number (singular/plural) barely relates to будь ласка.
IIUC, будь ласка derives from як буде твоя ласка “if there will be your favor”.
Ласка here is a noun (“favor”). Будь here is an imperative-mood verb “to be” (in Ukrainian, imperative mood is sometimes used as conditional mood, e.g: “…Май я… хоть який невеличкий заробок…, я би з Анною міг жити в Нагуєвичах…” (I. Franko) — literally “Have I at least some salary, I could live with Anna in Nahuievychi” with meaning “If I had at least some salary, I could live with Anna in Nahuievychi”).
Thinking about grammatical category of number:
Technically ласка is a singular noun. And theoretically you could put it in plural: як будуть твої ласки “if there will be your favors”, будь ласки, etc. But practically nobody says so; this phrase is too idiomatic, and you probably won't be understood is you change it in an unexpected manner; especially that the word ласка with meaning “favor” itself is rarely used in plural.
The whole phrase будь ласка can be used both as both singular and plural noun. For example, мені набридли твої «будь ласка» — “I'm tired of your ‘pleases’” (can mean either “I'm tired of excessive amount of your requests”, or “I'm tired of your excessive politeness”).