Open Document is not visible in F-53

Go to F110 and Check whether the Open Items of this Vendor are Blocked in any Proposal.
If it is so, Delete that Proposal and try making Manual Payment using F-53.

Stock Ageing Report

1- Enter the material number and plant in table MCHB.
2- Get the batch number from above step where unrestricted stock is not equal to zero and sort the enteries in ascending order of their created date.
3- Enter the material number, plant, movement type (101), batch number from above step in the table MSEG to get the material document number.
4- Select the last recent record by batch number from step 3. Delete the other records.
5- Calculate the date difference. Formula (Current Date - Material Document Posting Date).

FI and MM Integration

1- OMBA- This transaction is used for MIGO and FI Document Type configuration.
2- OMWB - This transaction will show the simulation of Material movement and FI GL Account Posting.
Check OMWD
OMSK - VGA with Account category link & Material type with Account category reference link as well
OBYC - for BSX Transaction event key check which GL assigned against your valuation class.

https://blogs.sap.com/2014/05/07/mm-fi-integration-a-conceptual-understanding/

https://blogs.sap.com/2014/05/20/mm-fi-integration-account-determination-simulator/