I would speak to the people who have created the extension. I would have thought given the Sense API they would be able to overwrite the variable value properly - but there may be a technical issue why they can not.
Taking input from an input box and writing a variable from it would require an extension, you may be able to modify the one you have downloaded, or find someone who can, but it is not necessarily going to be straightforward.
Again, you should be able to build (or find) an extension that will export a Sense table to a file, but it is not something I have done previously.
To do something in the load script is relatively straight forward, so if you have these data:
FROM lib://Data/Source.qvd (qvd)
If you wanted to have the Value by Dim1 in a table you could do:
Sum(Value) as Value
GROUP BY Dim1;
STORE ExportMe INTO lib://Output/MyFile.txt (txt);
DROP TABLE ExportMe;
The expressions can go beyond a simple Sum to being whatever you need to do. It will be problematic if you have data from different tables though. You will need to join these in the load script to be able to do calculations over them.
The only native supported export capabilities for Qlik via the store command are QVD and text no options exists to take data from Qlik and populate a database its not the sweet spot for Qlik. Searching for SQL Writeback capabilities within the community will yield custom solutions for this question.