Try tailscale for remote acess run it as a docker container. I csnt help you with the other questions.

Go with Qgis, there a loads of well written tutorials for using it and even step by step guids to do what you want: Example.

You can take ot a step further and host your maps online with either qgis2web like This, by using the build in tools or geoserver. You might even take it to the real world with qfield or an ar tool.