1) if TurboTax is correct that I could deposit $5.6K from my other account to the Roth account to make the converted Roth $20K total? Yes it is allowed ... your broker misunderstood you.... however
2) If yes to question #1, am I still within the window to put the $5.6K in the Roth account now? Sadly you have probably missed the 60 day window ... which means you have a taxable distribution. https://www.irs.gov/retirement-plans/retirement-plans-faqs-regarding-iras-rollovers-and-roth-convers...
