Normally the contributions are taken directly from your pay. This is how your employer should have set up the 401K contributions that you made. This way it is considered pretax.

So if it is not directly deducted from your paycheck when your pay check is made, then it cannot be used as a contribution to a 401K. So to answer your question, there is 0 days grace period or no grace period for contributions after you get your check. It must be pretax income

It depends on how the plan is setup and administered. Some plans call for quarterly deposits of your contributions and the employer's contribution. Some are setup as direct deposit from yours and quarterly for the employer's contribution. Check with the plan's administrator for details on how your plan was setup.