No electricity and the net is wrong.....

[xoxoxoBruce]

Do English-speaking people often use the sentence:That'all right.Thank you all the same.Could you please lend me 2 dollars?Sorry i don't know.and so on...Is there any short words to replace them?

Those are pretty basic sentences. It would be hard to make them shorter and still be acceptable WRITTEN English.
When speaking, we often use fragments or incomplete sentences, if it's a commonly used phrase. BUT, there is no way your teacher would accept that in an English class.
Is your teacher Chinese or foreign?