Besucher can be anybody visiting. Gast is more of an invited guest, say at a party or wedding.

It is acceptable but it's old fashioned and not in common use any more. For example words like doth and twas are probably not accepted but are grammatically allowed in the English language

The only time I've seen that is in the (very old) custom of tearing off petals of a flower and alternating between "s/he likes me" "s/he likes me not".

You might have heard "loves me, loves me not, loves me..." said whilst plucking daisy petals - perhaps it has Germanic origins... (sorry mmacinne for slight crossover)

Otherwise, you might have heard something along the lines of, "This is correct, is it not?" which is perfectly fine

DL gives the correct solution closest to your answer not the one it intended. It is a common problem and I regularly deal with it. Hearts are given for this purpose probably. Good luck.

Besucher for an all-male or mixed group of visitors, Besucherinnen for an all-female group.

If this sentence were "The visitors do not like me" then the verb would also conjugate differently, as it does in English: Die Besucher mögen mich nicht.

Yes.

"Mich" is used in accusative terms while "mir" is for dative.

Mich is like the English "me", mir is more like "to me".

(Accusative) Ex. Do you see me? Siehst du mich?

(Dative) I am well. Mir geht es gut. (literally: To me goes it good.)

/mɪlç/ (Milch with an L) and /mɪç/ (mich with no L) You're welcome

Yep, I almost did the same. The verb was the key.

Technically nothing, but it is not a common word in regular conversation at all. I would say the general population wouldn't even know the meaning of it.

Means the visitor is a ghost or supernatural being. It does appear to be a valid translation, though.

No. Only with nouns (not pronouns as is the case here). In this sentence we hence need nicht to negate the verb instead.