Could someone explain what is happening with the cases in this sentence? Is it ему because дайте takes dative? And минуту is in accusative? Thanks
Дать is one of the prototypal verbs that has both an object beign transferred and a "receiver" — a person to whom the action is directed towards. The latter is used in Dative. The resemblance of the word "дать" and "Dative" is accidental but they do come from the same Proto Indo-European root meaning "to give".
дать takes both accusative and dative, where the thing being given is in accusative and the person who it's being given to is in dative.
Does this mean the same thing as with English? So is it equivalent to, roughly, "stop bothering him for a minute"?
"Дайте" is formal speech imperative, "Дай" would be informal, right? So to my friend I would rather say "Дай ему минуту." instead of "Дайте..."?
Yes, дайте is also used for plural you. I think this sentence is aimed at plural you(informal), because пожалуйста is not used, which you would expect when you're trying to be polite.
How does дайте come from дать? If anything it looks like a second person formal conjugation, when this sentence would seem to need a third person form.
The second person plural is дадите. Дать is an irregular verb stem, to a degree.
As to the formation of imperative, it is always formed from the non-past stem. It is best to start with the 1st pers. singular form and remove the final sound (however, if the verb is an И-conjugation verb with a consonant mutation, look at the 2nd person singular and remove the mutation).
So, because of Дайте, which is a positive you command, this whole sentence, besides the verb is all direct objects? Ему being the person given the noun as posed by дайте, and then минуту js being that thing given unto the person, ему. I want to make sure I'm understanding it all.
The recipient of "give" is not a direct object in Russian. It is a textbook example of an indirect object expressed by the Dative case (in fact, Dative is literally "the giving case", from the Latin dō "give").
English has only one "objective" form, so verbs like "give" or "tell" are odd in that two seemingly equivalent objects are present. Semantically, in "give me a pencil" the two nouns "me" and "pencil" do not play the same role.
(of course, Russian also has a limited number of word forms available to fill in all the roles)