A power-on self-test (POST) is a diagnostic process that runs when a server is turned on to check the basic functionality of the hardware components and report any errors or faults. A POST code is a series of beeps or flashes that indicate the status of the POST process and identify any problems that prevent the server from booting up. A POST code can be heard through a speaker or seen on a display attached to the server motherboard. A POST code is useful for diagnosing errors without opening the machine or using any software tools.
References: CompTIA Server+ SK0-005 Certification Study Guide, Chapter 5, Lesson 5.1, Objective 5.1

When a virtual server crashes and presents a Purple Screen of Death (PSOD), the immediate response should be to document the incident. Collecting a screenshot of the PSOD is crucial as it contains error codes and state information that can be used for diagnosing the root cause of the crash. Noting the details, especially those that come after the line detailing the OS version, can provide specific clues to what might have caused the server to crash. This is a standard best practice before rebooting the server, as it ensures that there is a record of the event to investigate and potentially prevent future occurrences. A hard reboot should only be done after this critical information has been recorded.

A synthetic full backup is a backup method that describes copying only changed files each time it runs and using only a single file during a restore. A synthetic full backup is a backup approach that involves creating a new full backup by using the previous full backup and related incremental backups. This means that a backup solution does not have to transfer the full amount of data from the source machine and can synthetize the latest incremental backups with the last full backup to create a new full backup. This reduces the backup window and network bandwidth consumption. During a restore, only the latest synthetic full backup file is needed to recover the data. Open file backup is a backup method that allows backing up files that are in use or locked by applications. Full incremental backup is a backup method that involves performing a full backup first and then backing up only the changed files since the last backup. Full differential backup is a backup method that involves performing a full backup first and then backing up only the changed files since the last full backup.
References: https://www.nakivo.com/blog/what-is-synthetic-backup/
https://www.howtogeek.com/192115/what-you-need-to-know-about-creating-system-image-backups/

The most likely cause of the server crashing and the application being inaccessible is that the unauthorized software installed by the update is malware that corrupted the system files or compromised the security of the server. To restore access to the application while minimizing downtime, the administrator should scan and remove any malware from the server, and then reformat the server and restore the image from the latest back-up. This will ensure that the server is clean and has a working configuration of the application. Verified References: [How to Remove Malware from a Server]

The method that would help the administrator accomplish the task of creating new VMs in the shortest amount of time and meet the system requirements is template. A template is a preconfigured virtual machine image that contains an operating system, applications, settings, and other components. A template can be used to create multiple identical or customized VMs quickly and easily, without having to install and configure each VM from scratch. A template can save time and ensure consistency across VMs.