Kumusta!

Kumusta ka? Ako si Valerie. Amerikana ako. Gusto kong matuto ng Tagalog. Ang ina ng aking kasintahan ay Filipina.

Ginagamit ko ang Ingles at ang Hapon. Gusto kong gumuhit at sumulat. Ako ay nasa ika-dalawampu't tatlong gulang. Ang aking trabaho ay magturo ng programming sa mababang paaralan.

Salamat! Babay!

--

(I don't know how to say "I like writing" versus "I want to write"...)

-I like writing- Mahilig akong magsulat.

I want to write- Nais/Gusto kong magsulat.

I agree with Vincent's corrections.  However, in your second paragraph, though the grammatical corrections are OK, you may need to say them in other ways to be better understood.   

Ginagamit ko Ingles at Hapon.=> Marunong akong mag-Ingles at mag-Hapon.  (When referring to languages you speak, you use "marunong" (knowledgeable).  The "mag-Ingles/Hapon" translates to

“to speak English/Japanese”.  To use "ginagamit" (using) for languages would need the inclusion of a purpose.  For example, if your purpose is for writing, you may say, "Ginagamit ko ang Ingles at Hapon sa aking pagsulat." = I use English and Japanese in my writings/when I write.

Gusto ko gumuhit at sumulat. => Gusto kong mag-drawing (magdrowing) at magsulat/sumulat.  ("Gumuhit/Mag-guhit" really means to draw lines.  Though it may be contextually understood to mean drawing, I think the majority of us would say "mag-drawing" instead.  "Magdrowing" would just be the Tagalog way to write it, but it would rarely be written that way.  You may also use either "magsulat" or "sumulat", but the former would most likely the one used when speaking about writing as an interest.

Beintitres ako. => Beintetres na ako.  (The "na" makes it clear that you are referring to your age - I am already 23 (years old).   Without the "na", "beintetres ako" actually means "I am number 23".

Aking trabaho ay maturuan programming sa mababang paaralan. => Ang aking trabaho ay ang pagtuturo ng programming sa mababang paaralan. = My job is (the) teaching (of) programming in elementary school.  (To use "maturuan" would mean "My job obliges me to teach...".  To use "magturo" (to teach) is better than "maturuan" and may be used commonly enough, but still carries with it a sense of teaching being a duty. "Pagtuturo" (teaching) would be its noun form and a better term to use to refer to your job.) 

Though you will hear us say ¨babay¨, I don’t think we write it that way.  What we really are saying or might write is “bye-bye”.  Usually though, in writing, we just use “bye”.

Bye.  :-)