こんいちわは！

グズマンカロリナです。私はアメリカ人です。テレビガムが大好き！私は二十さいです。どうぞよろしく！

こんにいちはわ！(type: konnnichiha) *We write こんにちは but we pronounce it こんにちわ.

グズマン  カロリナです。私はアメリカ人です。テレビガゲームが大好きです！私は二十さいです。どうぞよろしく(おねがいします)！

*We accept that the foreign name is writen/said "first name" first and between the first and last name, we put "space", so it would be better to write カロリナ グズマンです, or you can also write: カロリナ・グズマンです。

*I would write 私は first: 私はカロリナ グズマンです。アメリカ人です。

*The Japanese counter is very complicatetd, so you don't have to worry about. However, "20 years old" is the irregular one, we say はたち. (I'm 20 years old = 私ははたちです。)

*どうぞよろしく！is correct, but it's the casual way. Since you wrote other sentences in the formal way, it would sound more natural if you use the same form. 

Hi, good job! Though I wrote many suggestions, please do not worry too much because our languages are totally different from each other. Please enjoy learning. I hope this helps you.