What you are primarily discussing is the hosting model for the underlying cloud you are using, for example, from what you have said so far your hosting model is relying on Infrastructure-as-a-Service (IaaS), and you want to have less responsibility for managing the Operating System.
That being the case you would need to move right in the table below to ...
From my experience this is very provider specific and requires evaluating the SLA offered for a particular service.
For example the siteground cloud server offerings shown at
https://www.siteground.com/cloud-hosting.htm state: We preinstall and maintain all the software you need on your server.
While offerings from liquidweb they make it clear they will ...
Do not trigger Build 2 automatically from Build 1. Instead add a last step to Release 1 to queue Build 2. There are a few ways to do it, e.g. https://stackoverflow.com/questions/52821204/how-to-queue-build-pipeline-as-task-from-release-pipeline