Is it possible to do this?

Yes—Excel can reproduce both behaviors, but the rules must test cells’ underlying values, not displayed icons. For the Level range, select the data cells, choose Home > Conditional Formatting > New Rule > Use a formula, and enter =$F2="Assigned"; set a red fill and adjust F and the first row to your sheet. If the icon is an inserted picture, keep “Assigned” in the cell or a helper cell and base the rule there. For Date Completed, select its range and create one rule per checkbox: =$G2=TRUE for light brown, =$H2=TRUE for gray, and =$I2=TRUE for red. Put rules in the intended priority and use Stop If True if only one color should win. Modern in-cell checkboxes return TRUE/FALSE; older Form Control checkboxes must first be linked to helper cells. Duplicate the completed template sheet so every employee tab inherits the validation and formatting.