Trying To Learn Mandarian!(1)

Hey, I shouldn't correct this as a native speaker will be able to give you the most natural sounding sentences, but I can point out a few things that might help you (from a learner's point of view)

你 好。你 好 吗?(nî hăo. nî hăo ma?)

你好。你好嗎？- You should not put spaces in between Chinese characters. 
你吃素吗?(ni chī sùi ma- are you a vegetarian?)
我吃与/肉/葡萄。(wô chī yù/roù/pùtáo- I eat fish/meat/grape)

Be careful with the characters you are using. I know that at the beginning it is almost impossible to read characters, but the more strict you are with yourself, the quicker and better you will get at recognising them! 與 - and/with 魚 - fish (as in the animal) 魚肉 - literally "fish meat" - the fish you eat. When you list things in Chinese, you should use this comma 、 so it should say something like 我喜歡吃肉、尤其是魚肉，也喜歡吃葡萄

1: 我 课(wô kè- I am thirsty)

課 means “class" - like the kind you attend at school. 渴 means thirsty. You can say 我渴 or 我口渴, both are OK 
2: 你 喝 水(nî hē shùi-you drink water) 

2:好的, 谢谢(hăode, xiexie-ok, thanks)

* 那 个 人没 关系(nà ge rěn , mèi guanxi- that person doesn't matter.)

I don't really know what you want to say here, I don't really understand your English. 

*我们 开心(/ 生气), 感 被(wômen kaīxīn/shengqi, gān bèi- we are haply(/angry), cheers!

我們很開心 - we are (very) happy / 我們很生氣 - we are (very) angry. In Chinese, there are two versions of "to be" - one for nouns and one for verbs. 我是人 - I am a person (noun) / 我個子很高 - I am tall (adjective) 

感謝 is used for when somebody does a really big favour for you or you win a prize or something. People usually say the phrase 非常感謝（你）. When I helped an elderly man in a wheelchair once he said 非常感謝你, while for "thanks" people just say 謝謝, or even just 謝拉！

I'll appreciate your corrections guys, 谢谢 :D

Trying To Learn Mandarian!(1)

你 好。你 好 吗?(nî hăo. nî hăo ma?)                      你好吗 this sentence a Chinese native speaker never say this. its wierd.
你吃素吗?(ni chī sùi ma- are you a vegetarian?)
我吃鱼/肉和葡萄。(wô chī yù/roù/pùtáo- I eat fish/meat/grape)

1: 我 渴(wô keˇ- I am thirsty)
2: 你 喝 水(nî hē shùi-you drink water) 请喝水（qingˇ heˉ shuiˇ  drink water please）
2:好的, 谢谢(hăode, xiexie-ok, thanks)

* 那 个 人没 关系(nà ge rěn , mèi guanxi- that person doesn't matter.)
*我们 开心(/ 生气), 感 被(wômen kaīxīn/shengqi, gān bèi- we are haply(/angry), cheers!

I'll appreciate your corrections guys, 谢谢 :D