No. TurboTax does not mail things to you. Transcripts come from the IRS.
You can get a free transcript from the IRS:
https://www.irs.gov/individuals/get-transcript
No. Only you can access and print your return. Why can't you download it? Or why can't you efile it?
How to mail a return from the Online version
When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s. Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS received the return. Don’t forget state.
Important! Mail Federal and State in separate envelopes and mail each year in separate envelopes.