Welcome to the forums !
To answer your question about MyFICO updates ~ any report/score pulled from MyFICO reflects what is on the credit report at the time that the report is pulled. So if items have been deleted from Transunion for example, any subsequent reports would reflect that the items are no longer showing.
The TU score sold here at MyFICO is FICO98, which is an older version of the FICO scoring model. Mortgage lenders almost exclusively use FICO04. The most current score version is FICO08 but it has not been adopted widely. There are still lenders that pull TU98 FICO scores, like Navy Federal Credit Union for example.