Do I have to have last year's return to file taxes online?

Answer 1

You may need your Adjusted Gross income from the prior year return to do the electronical signature. You would find this on last years return. If you don't have a copy of the return, you can call the IRS and after they verify your identity they can provide that information to you over the phone
Call 1-800-829-1040

Answer 2

No. But if your using an online program such as turbo tax, you will not be able to sign electronically unless you know the exact amount of your AGI from last year. Not a problem though, you will be able to print a sheet to sign and mail.