Help...

Ok, I have a few questions...
1: How do you write doki or dokin (like the sound) in japanese? (along with Chu)
2: I'm going to go visit my japanese cousions soon, and I want to know, how would you say:
-"Hi. Long time, no see."
-"Happy Birthday Musashi-kun" -"Happy belated Birthday Musashi-kun"
-"Thank you for teaching me."
3: and does "Mata aimashou" mean I hope we meet again.
and if so, how would you write it in Japanese?
4: and how would you write "But, you're the one I love..." in Japanese?

Thanks for your help in advance!

1: How do you write doki or dokin (like the sound) in japanese? (along with Chu)
4: and how would you write "But, you're the one I love..." in Japanese?
I don't understand the words/phrases you are trying to write. Any background and context for 4.?

2: I'm going to go visit my japanese cousions soon, and I want to know, how would you say:
-"Hi. Long time, no see."
Yaa. O-hisashiburi. (Hi. Long time no see.)
Konnichiwa. O-hisashiburi. (Hello, ...)

-"Happy Birthday Musashi-kun"
Tanjoubi omedetou, Musashi-kun

-"Happy belated Birthday Musashi-kun"
Chotto osoi kedo, tanjoubi omedetou, Musashi-kun. (Literally, "I'm a bit late, but...)

-"Thank you for teaching me."
Oshiete kurete arigatou.

3: and does "Mata aimashou" mean I hope we meet again.
and if so, how would you write it in Japanese?
Literally it is "Let's meet again," so the meaning is very close.
また　会いましょう。

For #1:
I was thinking like, the sound of your heart beating...? if that helps
and for #4:
I don't really know how to describe it...^^;
But thanks for the others!

1. If it's the heartbeat, it's どき (doki), or どきどき (dokidoki,) or どっきん (dokkin).
The last one would be like you are so excited it feels like it skips a beat :)
The above is in hiragana - you can also write it in katakana, as ドキ　ドキドキ　ドッキン

4. Is it said by a girl to a guy, or the other way around? And the way it's phrased "...but you're the..." sounds like a protest, so I thought I might ask for clarification.

it's said by a guy to a girl... :3

and thanks! :3 This helped out alot!

4: and how would you write "But, you're the one I love..." in Japanese?

- Demo, boku ga aishite iru no wa kimi nan da... (but it is you that I love...)
- Demo, boku ga daisuki na no wa kimi nan da...

Said by a boy to a girl. THe first one uses the word "aishite iru" to refer to love (serious kind), and the second uses "daisuki," a more common word used to say you like a lot/love somone, you fancy someone.