First, I think that the "Output file" which the Task Manager provides is just overwritten each time the Task runs (haven't verified this, but that's how I read the code). So there really is no history of the Task logs AFAIK. In any case, the Task Manager does not support any sort versioning or history of this output file.
My best suggestion is that you add a "Log Directory" Property to the Task definition, and then the OnTask() method can use that to manage output from the running Task. Perhaps a separate directory for each scheduled Task, and a date/time stamp as part of the file name? This does not give you any direct tie in or access from the Portal, but it should be pretty easy to identify the log for any given run.
I don't think this is possible with the first version of SAM. We've done some work on adding HTTPS support for the Alerts REST API, and I believe Prometheus can be configured to do HTTPS for the metric scrapes, but we need to look at the Portal connection as well.
Yes, this is the System Monitor. I believe it's always started by default, but it can be stopped manually.
It does monitor the size and growth rate of Journal files. But it also monitors for long running Transactions, which may be the journal reads you're seeing.