Notice Period Duration
Normally, the notice period is one month, but in most organizations, it can be 2 to 3 months at the senior level, i.e., Manager and above. This is specifically to avoid a vacuum because finding a suitable person at the senior level takes some time, hence this procedure exists.
Leave During Notice Period
Regarding availing leave during the notice period, it differs from company to company, and most organizations don't allow it. However, in case of exigencies, the employee is allowed to avail leave, but in that case, the notice period is extended. For example, if the notice period is for 2 months and an employee submits their resignation on the 15th of March with the last working day set as the 14th of May, but the employee is allowed to take 6 days of leave, the last working day would be the 20th of May.
I believe that a resigned employee may not have as much interest in the work, and in some cases, such employees may disrupt the culture. Therefore, it's better to relieve the resigned employee at the earliest.
Hope this clarifies things.
Thanks and regards,
Kamesh