Sonnet 116 isn't English, it's Old English. Most English speakers either can't understand what Shakespeare wrote, or they do so with great difficulty. I'm struggling to figure out what that sentence means. "If that be the case..." isn't correct English, but it sounds good when spoken with a pirate accent (which is why pirates speak like that in fiction). Both instances of "You'll be..." work like normal English.

It is actually heard . from time in American English to express the possibility of a situation to exist. It's the present subjunctive and it's correct, but not common. "There might not be beer at the party." Well, if that be the case, I might as well stay at home.". A situation that may or may not exist.

It is literary English. You won't need it for modern English.

"IF THAT BE so, I shall have my head examined" the judge ridiculed at the prosecution's far fetched scenario. It's correct English. It depends on the class of people you are talking to, the educated or the not so.

Mojave made a good comment above: it's the present simple subjunctive. In both of your contexts, the speakers (a poet and a pirate! yarrr) use this form more freely than an average modern English speaker would. Still, it's perfectly correct grammar. Basically: "I am / we,you,they are / he,she,it is" = indicative mood, ie. it exists in reality. However, "(subject) be..." = subjunctive mood, ie. it exists in theory. A modern speaker would prefer "If that is" over "if that be", but both are grammatically correct.