We want to put a value into a table with the command "Set", e.g.
Set cell[Table,7,5]  "x"
Instead of specifying a certain row and column, we would like to put the value into the table cell we point at with the mouse cursor. Can this be done?

You can use the system variables &V[_tabrow] and &V[_tabcol]. For example:
Set cell[Table,&V[_tabcol],&V[_tabrow]] "x"