Do you need the previous year's tax receipt to file the current tax?

Yes, you may have to show your previous tax documents, if you're not new to US. However, your tax requirements may differ from your previous year if your income has increased or decreased, you've moved to a new place, and so on.

Yes. You'll be asked to give the copies of your income tax returns from previous years.

Yup, you need to show the documents to prove your prior tax payments.