The short answer to both questions is yes, they can, but to do so can be very dangerous. If an employer starts paying a salaried employee more when they work more then that employee may have just been treated as an hourly employee. When an employees wages vary depending upon the number of hours worked in the payroll week, the employer is treating the employee as an hourly employee (non-exempt). When an employer treats an employee as hourly (non-exempt), they become hourly (non-exempt) permanently and are then entitled to overtime at 1.5 times the average rate for the payroll week. So if an employer pays an employee more one week because they worked extra (over 40) hours, the employee is no longer an hourly (exempt) employee and is entitled to overtime. There is no prohibition to having salaried employees clock in and out, but using those hours to pay more or less will be very costly to the employer.
Can your employer dock your pay if you are salary? The short answer is again yes, but to do so can very dangerous. A salaried employer can only have their pay docked for very specific reasons. For example if you are salaried and miss a whole day for something other than sickness or accident (personal reason) then that whole day can be docked. There are other reasons that an employer can dock pay but to do so improperly (or if done on an hourly deduction) can make the employee change from salary to hourly and subject the employer to overtime.
If an employer docks the pay of a salaried employee that employee should seek legal representation to see if that is legal under the Fair Labor Standards Act. As an employment lawyer in El Paso, Texas we see many employees who are improperly classified as salaried when they should be hourly as well as salaried employees who have their pay improperly docked.