Learn English – “Having me stay”

I wouldn't say that either is wrong, but 1 could do with some improvement. I'd recommend changing it to:

I'm just here for a month.

A likely reason that the third sentence sounds 'wrong' to the other person is that "I will" hasn't been shortened to "I'll", like it commonly is. I'd recommend shortening your "I will" and "I am"s to "I'll" and "I'm"s respectively.

"There are myriad" and "there are a myriad" are both correct, and in fact NGrams shows that both are far more common than the "there is" and "there's" variations.

Some weird logic has been used by some people here to suggest that "myriad" has to be singular, even though everyone would say "There are a thousand".

(In British English, collective nouns are frequently treated as plural, but even American English regularly treats numerals and expressions like "a lot" as plural.)

"There are myriad combinations" (where "myriad" is an adjective) would probably be commoner than "there are a myriad of combinations", but both are correct.

"There is a myriad of combinations", with singular agreement, should probably be regarded as correct, too. But even if it weren't, "There's" would still be acceptable colloquially, in the same way that "There's hundreds" or "There's five" is generally accepted colloquially, even though formally it should be "There are hundreds" and "There are five". ("There're" is not often seen written down, though some people say it.)