Hi,Anaya, your pinyin is very good , i wrote something about this passage.The green words are your original sentence,orange words are those i think not used properly. others are my view. You can have a look and i hope it can help you.

Zao an〜! Wo xī wang nin you yi ge mei hao de yi tian.早安！我希望您有一个美好的一天。(That's a good sentence)

”Wo zuo tian you yi ge wei da de ri zi, dan wo hen pi bei ao ye."       I think you wanna mean"Yesterday is a great day, but i'm tired cuz I stayed up late." If it is that meaning, then it should be "Zuo tian shi yi ge wei da de ri zi , dan wo hen pi bei , yin wei wo ao ye le." in character is "昨天是一个伟大的日子，但我很疲惫，因为我熬夜了“

Jin tian, wo ji hua zai shi xing wo ban de jiang hua zhong. Zhu wo hao yun!    the word" zai" means "-ing", the "zhong" here means "in", so the two are unproper. I think you wanna mean"Today I'm going to have the speech in my class, wish me luck!" translated intot pinyin is"jin tian, wo yao zai wo ban jin xing ji hua zhong de jiang hua , zhu wo hao yun!" in charaters is "今天，我要在我班进行计划中的讲话，祝我好运！"

Wo yi jing zuo le hen duo gong zuo.  That's a correct sentence, translated in characters should be "我已经做了很多工作"。

Xue yuan shi fei chang kun nan de, yin wei wo yuan li wo zai niu yue de jia tíng. 

I'm not sure what you want to mean by"xue yuan", i guess you wanted to say" learning language" or "being a student". if it's the former, then in pinyin the sentence should be"xue yu yan "; if it's the latter, then "zuo yi ge xue sheng",,,translated in characters is"学语言（or做一个学生）是非常困难的，因为我远离我在纽约的家庭“

Mu qián, wo zai yi suo da xue, li wo jia shi 6 xiao shi.  correct sentence,except for the last part, and the order is unproper, i think ”mu qian, wo zai yi suo li wo jia shi 6 xiao shi che cheng de da xue" is better. "目前，我在一所离我家十六小时车程的大学。“

Wo jin wo suo neng.  it's quite excellent that u can use this phrase.我尽我所能。

Da jia shui yu wo dui zhong wen de yan jiu jiang you zhu yu wo he ni suo you zhi chi wo,Actually i can't understand "he ni suo you" clearly, what do you want to express??

wo zhong xin gan xie ni.  correct sentence,我衷心感谢你。

bye-bye