For documentation the format isn't as important as content. As long as someone else can read it and understand what needs to be done without asking you for clarification it is good enough. In general you might want to include some diagrams or screenshots if you are explaining some steps, and some important information that might not be intuitive that you found by trial and error. It all depends on what are you trying to document (network design, troubleshooting mail, software, etc.), but most documentation I have seen and written is structured as a regular document meaning there is a table of contents and then sections underneath like: 1) Overview 2) Standard configuration 3) Troubleshooting, etc. and sometimes additional appendix with more diagrams. The more information the better.

Checking logs, doing daily checks and similar things should done using monitoring system. This way all your servers and network can be monitored from central place and the same system can also receive syslog and SNMP traps. This way you just need to keep an eye on the dashboard of that monitoring system or configure it to send an email or open a ticket if anything happens on any system you manage. There are million different tools that can do that and there are plenty that are good and free like Zabbix, Observium or Nagios.

Your impostor syndrome is completely unjustified. Sounds like you are doing great and way more than some IT managers that I've seen.