It's not usually proper to start with 'me'; it's considered egocentric to say "It's a letter for me and you..." or "It's a letter for me and John..."; you should say "It's a letter for you and me..." or "It's a letter for John and me...".
However, you can use poetic license for effect, such as "Me and you and tea for two...", or "Me too, me too. I want some..." or "Me? You talkin' a me?".
NO
No, a sentence can begin with any kind of word. The first letter of a sentence is always capitalized to mark the start of the individual sentence, not because the word is a proper noun.
Yes.
Yes, it is proper English to start a sentence with the word "oh." This interjection can be used at the beginning of a sentence to express a range of emotions or to call attention to something specific.
No, because "and" is a conjunction, which is a word that puts together phrases and clauses to create a sentence.
No, because "and" is a conjunction, which is a word that puts together phrases and clauses to create a sentence.
No, the word cholera does not have to be capitalized unless it is the start of a sentence or part of a proper noun.
No, unless it is the first word of a sentence or part of a proper noun.
No, you should not. You should only capitalize a word when it is at the start of a sentence or when it is a proper noun.
You can begin the sentence with a modifying adverb clause. "With the proper care, many mistreated dogs will recover."
No, "diabetes" is not capitalized unless it is the first word in a sentence or part of a proper noun.
No, why should it be? Well if it's at the start of a sentence, but really, how many sentences start with the word example?