Are there rules about how quickly it has to be deposited?
Be warned do not use the 15th of the month as a safeguard. The view is as soon as administratively possible. If your plan is ever audited and you made a deposit the 4th day of the month then they will assume all deposits can be done that timely. The moral of the story is as soon as administratively possible and keep those deposit dates consistent.
Typically this deposit should be made immediately - after all, the money belongs to the employee. The latest date that the money should be deposited in the account is set by ERISA as "no later than the 15th business day of the month following the month that the employee contributions were withheld from pay."
The guidelines state no later than the 15th of the month following withdrawal from pay, OR as soon as reasonably possible. I recently advised an employer that was making 401k deposits weekly as payroll was cut that wanted to switch to monthly deposits not to do so. The reason is that they had already established that weekly deposits were reasonable for them, so this employer would have to jsutify why weekly all of a sudden became unreasonable.