Can I print/save supporting forms in Turbo Tax Deluxe such as Interest & Dividends, etc.?

What do you mean by supporting forms? The forms you receive from others such as W-2s and various 1099s are never entered directly into TurboTax so it is not possible to save those forms in TurboTax. The information you enter from those forms is generally entered on a tax form or worksheet and those forms and worksheets can all be saved in the full tax return with all forms and worksheets. 

If you want all the backup worksheets,  Try printing from the Print Center

Log back in your TurboTax account and "add a state" to open the return back up (you are not really adding a state, just to open it back up), then

Click on Tax Tools on the left side of the online program screen. 

Then click on Print Center. 

Then click on Print, save or preview this year's return.  Choose the option Include government and TurboTax worksheets