I think you met the trouble because the setences you read are not pefect in grammar. Example 1: 我等不及要告诉她。我等不及了要快点儿离开学校，去享受夏天。 了 is a structural word in Mandarin expressing a meaning of 'something you did is over' and symbolize the declarative sentence is over. For example, 我吃饱了 or 她离开了. In these two sentences the movement 'eat' and 'leave' has finished, and they're two independent sentences. In the same way, 等不及了 is an independent sentence in structure. But 等不及 is not a sentence but an adverb. For instance, 我等不及去大吃一顿了, or 我都等不及告诉她这个好消息了. So 我等不及了要快点儿离开学校 is not perfect correct in grammar, you need not use it as a model. Example 2: 我等不及想要读这本书的最后几章了。 我迫不及待地想要顺流而下，在河上度过整个下午。这些兴奋的孩子迫不及待地想要去迪斯尼乐园。 迫不及待地 is an adverb too, and it's similar to 等不及 which means 'can't wait to do something'. In the three sentences of example 2, you can replace 等不及 with 迫不及待地，or the contrary, without changing meaning of the sentences. The only difference between them is that 迫不及待地 is formal and 等不及 is colloquial. Lastly, when you replace 迫不及待地 with 等不及, you'd better add 了 in the end of the sentence to make it sounds fluent, just like 我等不及想要顺流而下，在河上度过整个下午了。 or 这些兴奋的孩子等不及想要去迪斯尼乐园了。

首先，两者的意思相近！但不完全相同。“等不及”和“等不及了”区别在于后者多了一个字“了”的后缀。表示：情感的抒发不同。要区分在不同的句子中，它们的意思是否属于重要，或者说不同的句子所表达的关键性不一样，所以要求的语气会分重和轻。“迫不及待”是中文中属于成语，在口语和书面语当中是有区别的。“等不及”一般用在口语化的句子当中。中文的语法很复杂，对于这种情况，建议你把他们归类为同性质的，这两者的关系很微妙，一般只有中科院的那几个专家才能细致的区分！so，don't bother ！

there is little difference between 等不及(了) and 迫不及待地,generally,both of them when you use in your sentence are right,if you aren't the one studying Chinese ,there is no need to distinguish them so clear.they just like english words "want to " and "wanna"

first 我等不及要告诉她。 我等不及了，要快点儿离开学校，去享受夏天。both ok. i think you can also add a dot between "了" and "要" , like this: 我等不及了，要快点儿离开学校，去享受夏天。 了=放在动词或形容词后，表示动作或变化已经完成。such as 喝完了，醒了，长高了 second 等不及 and 迫不及待地: 等=待 迫=urgent 地=to so 迫不及待 is more urgent

你误解了我的意思，我的意思是“等不及（了）”和“迫不及待地”是同义词，英语里面不是也有同义词吗？