That is because the transaction you show is a receipt. If it were a payment, the same field would be labeled Payee.
Yes, just as on every other transaction form in Manager. On transaction lists, the contents of this column is the summary-level description. That is consistent, as the other is at the line item level, which is not displayed on transactions lists.
Your Notes box is a custom field. You can delete it under Custom Fields in Settings, assuming you have not used it on any transactions.
Contact is used throughout the program on drill-down transaction lists, because all these are displayed with the same code. Some places, this is a payee, others a payer, sometimes a customer, elsewhere a supplier. Contact does not conflict with any field or variable name and covers them all.