#1 both a and b are correct and well as #2 a and b. #3a is correct but b is not correct for a teacher with the choice of the verb "direct" since it could be taken as administer, manage, supervise, command, order, etc., being then improper for the context of a teacher.

I suggest a change to your question: "...or how is IT BEST to use them?" Don't forget "thougt" is spelled "thought," "Seee" is spelled "see," and we capitalize "I" when it's a pronoun.

Excellent question! Yes, see, watch and look are very close synonyms--at times being direct synonyms. Yet, there are specific situations that would be best for each. "Watch" is directing the attention and gaze to something for an extended time as the TV, play, sports game; always something with movement (so not a newspaper or book). "Look" is directing the gaze for an unspecific amount of time, usually short and especially in the context of an imperative command ("Look what I can do!"). "See" has a particular focus on the eyes and their capability of perceiving light, images, etc. and focusing, directing your attention on something visible. It also relates to perception of meaning at times like "I don't see what you're getting at". I recommend reading a good dictionary entry (with examples) for other meanings and explanations too numerous and in depth (and much better than I can explain!) to put here.

Good question! Not much written about it--even the Oxford English Dictionary doesn't address it. However, they do on dictionary.com and they say that it began to be capitalized in the mid 13th century "to mark it as a distinct word and avoid misreading in handwritten manuscripts." I assume from then on it just became normal in English. Odd though since no other pronoun is capitalized! Maybe philosophically that points out the tremendously strong urge within ourselves to be selfish and self-exalting (not a good trait!!).

I agree with Michael's solution. I would just add that despite it being common around the UK I do not think it is so common in the United States. We might think of someone ushering people in through a door into a house and so to see in the New Year may sound funny to some. I think it's more recognizable in the US to say "to ring in the New Year" (although that logically also may sound funny) or to say "to bring in the New Year" (also funny if you think about it, like you are carrying it in).

Serge, as far as I can tell, the difference does exist in Russian: other = другой another = ещё один I would only further explain in addition to what others have written that "another" is a compound of "one" with "other" and would be for situations especially pertaining to quantity. Sometimes another and other are synonymous.

The first sentence is normal--I just might add a "that": "How come this is the first that I hear of it?" The second is not normal in my opinion. I would rephrase it as "How come this is the first time I'm seeing it?" or "How come this is the first time that I'm seeing this?"

1 and 3 are just fine. #2 is understandable but not normal. I would suggest "I mustn't cut class and I must focus on studying." "Buckle down" is understandable in such a context, and maybe it's normal in the UK but it may sound odd in the US.