Two quick questions:
* What sort of tasks will a Linux systems administrator do in a typical work day?
* Is it possible to get hired as a Linux system administrator if you are over 50?
The responsibilities of a system admin cover a large rang of activties. The admin is responsible to assure machines and their services are operating at their level. This will mean, troubleshooting hardware, upgrading hardware, upgrading operating systems, supporting new operating systems, configuring operating systems, writing code for automation, network and system security configuration, data-recovery, user and application monitoring, etc. The list goes on. I would google "roles of a linux system admin" to get a wide view of this discipline.
Yes, you can get hire at the age of 50. You may want to research age requirements to be sure.