我看了一只老鼠！（我看到了一只老鼠！）

这个上午我看了一只老鼠(今天上午我看到了一只老鼠)！我是了真的害怕（我真的非常害怕）。马上我找到了我的猫就我抛了它对这老鼠（我就立刻找到了我的猫，把它抛向这只老鼠）。猫只走开（但是猫就这样走开了）。我的猫很懒和没用的（它很懒很没用）。
This morning I saw a mouse! I was very scared. Immediately, I found my cat and threw it at the mouse. The cat just walked away. My cat is lazy and useless.

Corrections are good but explanations are also good.

In Chinese , when you typed 这个上午, you are announcing a topic, so everything that follows is about that time frame, unless you introduce another topic. This means, the thinking that you were afraid is already covered by "this morning ..." Further, adjectives can act as verbs ... so in English, we say, I am afraid. In Chinese, I 很 afraid (some adverb must go in front of the adjective. 是 is only used to connect nouns. I am a doctor. I am a student ... But not, I am afraid. 

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The reason why people took away your "就我抛了" is because 就 goes in front of a verb, and since you already mentioned 我 in the first half of the sentence, no need to repeat it in the second half. Besides, 把 acts like a verb and is even translated as such. 把 structure is 把+ noun or noun phrase + verb + compliment ... must be two characters ... and action verb.

我看了一只老鼠！

这个上午我看了一只老鼠！我是了真的害怕。(In Chinese, we do not use 是 before adverbs and adjectives except for strong emphasis.) 马上我找到了我的猫，就我抛了把它对这老鼠抛。但是猫只走开。我的猫很懒，和很没用的。(It sounds a little better this way.)
This morning I saw a mouse! I was very scared. Immediately, I found my cat and threw it at the mouse. The cat just walked away. My cat is lazy and useless.

你好：艾利森！Nicely written. Be aware of word order rules in Chinese, as they are different from English. When you want to say that you threw your cat at the mouse, the order is 把它对这老鼠抛 (literally: hold it aimed at mouse throw). Think of it this way: in Chinese, we always setup the situation before we mention the action.

Also, 我希望你能快速解决这个问题。老鼠是很讨厌的！ =\

我看见了一只老鼠！

今天上午我看见了一只老鼠！我很害怕。我马上找到我的猫，把它抛到老鼠跟前。但是猫却走开了。我的猫是很懒又没用的。
This morning I saw a mouse! I was very scared. Immediately, I found my cat and threw it at the mouse. The cat just walked away. My cat is lazy and useless.

我看（见）了一只老鼠！

这个上午我看（见）了一只老鼠！我是了真的害怕（了）。马上我找到了我的猫，就我抛了它对这老鼠（把我的猫抛向老鼠）。猫只走开（了）。我的猫很懒和（也很）没用的。
This morning I saw a mouse! I was very scared. Immediately, I found my cat and threw it at the mouse. The cat just walked away. My cat is lazy and useless.

1.“看”means look at .     "请看图画，你看见了什么？"     Please look at the picture, what did you see.

2. "害怕" is an adjective. "了"should be added after adjective/verb.

3.Subject +把+Object +V+.......          The structure indicates that an action  is applied to somebody or something with the emphasis that the action will bring about a result  or influence.      "把我的猫抛向老鼠"，The action is "抛"， and the result is "猫和老鼠在一起了"。 so you need to use“把” in this sentence.

4.“猫只走开“， The verb is "走开".and the action is done when you talk about the thing, so you need to add"了" after  the verb ”走开“.

5.又懒又没用= 很懒也很没用.    means  lasy and useless.