I'll try make a few changes to the original thread list, if I may:
です[desu]
The polite copula; goes at the end of a sentence equation one thing to another.
と [to]
Basic word for "and", used within sentences. わたしはりんごといちごがすき。 [Watashi wa ringo to ichigo ga suki. -> I like apples and strawberries.]
なに [nani]
General "Say, wuh?" ("What?") on its own, but can also be used in sentences. Usually if you what to use "what" in a sentence, in its common English sense, なん [nan] is the better word. これはなんですか。 [Kore wa nan desu ka. -> What's this? (Polite)]
あした [ashita]
Tomorrow. じゃ、またあした、ね。 [Ja, mata ashita, ne. -> Well then, see ya tomorrow, okay? (Informal: probably heard it in anime - sure as hell I have.)]
きょ [kyo]
Today. きょはげつようび。 [Kyo wa getsuyoubi. -> Today is Monday.]
Pronunciations for numbers:
1: いち [ichi], 2: に [ni], 3: さん [san], 4: よん or し [yon or shi], 5: ご [go], 6: ろく [roku], 7: なな or しち [nana or shichi], 8: ひゃく [hyaku], 9: きゅう [kyuu], 10: じゅう [juu]. Where more than one pronunciation is given, the first is most common in my experience. Learn where to use which case by case.
おはようございます [Ohayou gozaimasu]
Good morning, set phrase.
こんにちは [Konnichiwa]
Good day, or general "hello", set phrase.
こんばんは [Konbanwa]
Good evening, set phrase.
おげんきですか。 [O-genki desu ka.]
Are you well? How are you? This is really polite.
Between equals だいじょうぶ [Daijoubu] is far more common, which can be used both as a question with rising intonation, and as an answer with an afirmative tone.
げんきです。 [Genki desu.]
I'm well, quite polite, again see だいじょうぶ [Daijoubu].
おなまえはなんですか。 [O-namae wa nan desu ka.]
What is your name? This is very polite, in most cases you could just say あなたは [Anata wa] with a rising intonation, prefixing it with "sorry", すみません [Sumimasen], to soften it's harshness a tad.
There are many ways to answer this. In most cases, if it's clear you're the person being talked about, you may skip the whole わたしは [Watashi wa], just saying NAME です [NAME desu]. There are more polite ways, but generally you won't need these.
Generally, a polite introduction will go like this:
はじめまして。わたしはadamcubeです。どぞうよろしく。 [Hajimemashite. Watashi wa adamcube desu. Dozou yoroshiku. -> Pleased to meet you. I am adamcube. Please treat me kindly.]
There are infinite variations to work with, depending on social status, but you won't go far wrong with that general one.
はい / いいえ [Hai / Iie]
Yes and No. Be careful with the pronunciation of いいえ [Iie]; if you fail to stress the double "i" then it becomes いえ [Ie], or house.
わかります / わかりません / わかりますか。 [Wakarimasu / wakarimasen / wakarimasu ka.]
I (he, she, it, ect.) understand(s) / I (he, she, it, ect.) do(es) not understand / Do(es) you (he, she, it, ect.) understand? For the most part, in rudimentary Japanese speech, subject is ambiguous, and is understood from content.
ありがとう / ありがとうございます [Arigatou / arigatou gozaimasu]
Thank you / thank you very much.
どもう [Domou]
Thanks.
The above two can be combined for greater politeness and emphasis; どもうありがとう / どもうありがとうございます [Domou arigatou / Domou arigatou gozaimasu -> Thank you so much / Thank you so, so very much. (Haha - these are horrible approximations!)]
おねがい [Onegai]
Please. This actually means a wish or request. Add -します [-shimasu] to the end, and the translation is "please do it" or "please take the discussed action".
いくらですか [Ikura desu ka.]
How much is it (that)? Talking to a taxi driver: しんじゅくまではいるかですか。 [Shinjuku made wa ikura desu ka. -> How much is it to the Shinjuku district (of Tokyo)?]
どぞ 「Dozo]
Please, go ahead. This has several meanings, but usually indicates "you first" in a polite sense. It could be said allowing someone to pass through a door ahead of you, or when handing them a drink. Keep in mind that it is very polite; you probably won't hear it that much between equals.
わたしとたべませんか。 [Watashi to tabemasen ka.]
Won't you eat with me? Would you eat with me? The "shi" sound in わたし [watashi] is often softened in fast, fluent speech, leaving a sound like "watash to". This should not be said on purpose, you will find naturally that as you speak faster, the sound will soften naturally.
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That's just a list of important ammendments to your original list, as I see them. I reserve my right to be wrong - someone who knows please say if you find mistakes! It can only help me learn.
I also think that your last phrase should be: こんにちは、わかりますか。 Remeber that Japanese does not use question marks. Also, you need to include the extra ん [n] consonant in こんにちわ [konnichiwa].
じゃ、またね。