Retirement tax questions

You have it mostly right, but the initial ROTH funds came from two different custodians of the respective 401(k) account that I held - neither were TDAmeritrade. The first custodian sent me an overnight check that I immediately hand carried to TDAmeritrade, and in the second case the custodian did an ACH transfer directly to TDAmeritrade.   So this was not a totally "in house" issue.  They admit it shouldn't have happened, but I put the account number on the check for the transfer in, and I gave the account number to use for the ACH transfer.  I am sure that COVID had some bearing on it with limited staff to check things.