On issue is that the transaction types in the IIF file are wrong.  A "PAYMENT" is a customer payment on account and will always use an A/R account on the SPL line, and never "Unknown", unless you've named your A/R account "Unknown".  Also, each Payment should use a known customer name in QB.

It is unlikely that your bank will have any knowledge of your PAYMENT transactions, which won't use your bank account directly.  PAYMENTS should not be in an IIF file from a bank.

Also, unless you have named your bank account "[removed]-Demand Deposit" then the remaining transactions, which can be imported, will be imported into that account.  Really, the bank should ask you what your bank account is called and put that in the IIF file.

QB is auto-creating new accounts when they are encountered in the file.  Since they're not explicitly added, QB adds them using the default type, which is bank.