Using a value on a form as criteria in a query is done by referencing the control of that form in the query field criteria section of the query builder.EG On a form, Form1, you have a combobox, cmbName. On the query in the criteria section under the Name field you would put in =Forms!Form1.cmbName.
What do you mean by run, and save that query then update it in the form? If you want to save the query as a new query, you could use the CreateQueryDef method. To update it in the form wouldl mean changing the forms RecordSource to the name of the new query.
Calculations can be done in the query. Just select an empty column in the Query Builder, and click the Build icon on the toolbar to bring up the Expression builder box.