When you say you are an American, that is speaking in the present tense of who you are today.
Not sure what this means... consider rewording. Also, you go from "you" to "that" from first to second clause and it makes it awkward.
"To say, "I am American" indicates your current nationality." Idk maybe somethign clearer like that...
my family never celebrated much of our heritages backgrounds as much as I would have liked.
Wordy and again weird to read. "my family never celebrated our heritage as much as I would have liked."
Although I have a lack of culture in my life
Although I lack a cultural background... just a thought but saying you lack culture makes you seem bland, because anythign can be considered to have culture.. "sports culture" "hip-hop culture" and the like...
I now have a strong desire to experience and be apart of other cultures, and I am especially interested in Asian cultures such as Japan.
Poor sentence. you used culture twice, so it reads as repetitive and I would remove and I am and interested in..."especially Asain tradition" also.. isnt it a part not apart? not sure but check that..
MAJOR PROBLEM!!!!!
Read your essay from the point of "Although I have a lack of culture in my life" and count the times you say culture... it is actually ridiculous, and makes your essay terrible (sorry, but its true) you need to find a way to fix this, or you will, not get in. Just read it out loud to yourself and make sure you don't repeat anything too often (also used other in there at one point that bothered me.)
Your ideas are good here, and with just a couple of small tweaks you will have a solid essay, but you need to make those changes.