I actually taught this at school today. ;) 1) The structures are, "both of them know" and "neither of them knows". In these cases, we are talking about two people but "both" works as "they" (plural), and "neither" works as "he/she/it" (singular). 2) "Either way" is a set phrase. It means "no matter what happens" or "no matter what choice I make". If you want to use "neither way", then it becomes part of the statement and you must remove "it" ("neither way is..."). Pay attention to these small words. :) 3) "Hardly any" and "few" are synonyms, but "hardly few" doesn't exist.

1) "have asked them both and neither of them know the answer" is a negative sentence that means both of the people do NOT know the answer. "I have asked them both and both of them know the answer." is a positive sentence that means that both people DO know the answer. In slang we native speakers might say [they] 'knows' but the correct conjugation would be [they] 'know' because it is third person plural. 2) 'Either way' means it is actually expensive in both cases of travelling by plane or train. 'Neither way' means that it is NOT expensive to travel [either] by plane or train. However, if you say this you must omit the word 'it' - i.e. you would need to say: "neither way is very expensive [correct]" NOT "neither way it is very expensive [incorrect]" because this is confusing in regard to what 'it' is referring to. 3) Both are fine and have overlapping meanings. "Hardly any" has a bit more of an emotive undertone that the speaker expected more people to claim to have seen a UFO than did. "Few" in this context implies that a small number of people claimed to have seen a UFO (and depending on context of the surrounding story this could also carry the expectation that more people would have claimed to have seen a UFO than did). I hope this helps.

'Neither' means 'not one or the other of the two people or things' (Determiner and pronoun. Sometimes used as an adverb when the alternatives are introduced with the use of 'nor'.) 'Either' is used before the first of two alternative things. (Conjunction and adverb) Used in the negative as an adverb: 'I don't have any either.' 'Any' is used to refer to an undefined number (one or some) of things/people (Determiner and pronoun). This is usually used with negative statements or in questions: 'There wasn't any milk at the shop.' 'Have you got any money left?'