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1.  Familial relations are defined from one's perspective, hence unlike in English, we don't say "My father".  Exactly the same logic you used in your English version.  In Chinese culture, father comes before mother, from the older to the younger etc.  Though what you expressed is not grammatically wrong but very Un-Chinese.

2.  学 = learn, 学习 = learn and practise.  You can 学医科 but cannot 学习医科 because you are not licensed to do so.  Therefore you use 学习 only for certain things like learning martial arts, playing a musical instrument.

3.  The English "think" has several meanings, so simply getting the equivalent from a dictionary can be quite dangerous.

4.  interesting = 趣, meaningful = 有意思

5. "Going to a restaurant" is figuratively speaking in English but in Chinese, it can mean literally. 

These are the cultural nuances.  Good that you have an English version so my correction is more intuned to your intent :)

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我是 Jeanine。 我的家有五个人。 我妈妈， 爸爸，两个姐姐和我。我姐姐有一个孩子。他很可爱。我喜欢听音乐，看点影电影和游泳。我也很喜欢看中国点影电影。我是（一名）老师。我学习汉语（已经）四个月了。我想（觉得）学习汉语很有意思。今天我不忙。所以今天我和我的朋友去饭店。我门们喜欢去中国饭馆餐馆或饭店。他的吃反他们的菜很好吃。

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加油，超棒。

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my mather, father, son, friends, family, home =我妈妈，我爸爸， 我孩子，我朋友，我家。without 的

Chinese food, 中国菜， not 饭。 eg. American food美国菜, Japanese food，日本菜。

门，means door or gate。we 我们

Excellent  job, only 4 months you can write such a lot sentences in Chinese.  

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