you already have the rowId you want to update, so you only need to tell the grid to set the values on the columns you want, and mark the row as updated for your dataprocessor to detect the change
function doOnCheckBoxSelected(rID, cInd, state){
if (state=='1'){
alert("date approved");
}
var currentDate = new Date(); //This is just an example, here you can generate the Date in the format you wish.
/*Here goes the column index in which the date or status are...
In this case I'm assuming in the column 3 is the Status and in 4 the Date of approval, change them to your
real indexes*/
grid.cells(rID,3).setValue('Approved');
grid.cells(rID,4).setValue(currentDate);
dp.setUpdated(rID,true); //You tell your dataProcessor that the row was updated, so it mark the row as updated
return true; //if i recall correctly this is needed for the function to end correctly, maybe not
}