I see how to save a map area offline, but how can I make sure the markers layer on"my maps" is saved for offline use? I see how to view it as a layer, but are all the layers saved for offline use? (Seems unlikely and a waste of resources.) How do you save a select few for offline map use?
It seems to me that you are talking about your "Starred locations" when you're talking about the markers layer on "My Maps", eih? These are stored in Google Bookmarks and can be exported -- including the locations.
There's a good free tool, http://gexport.somee.com, available to convert the exported bookmarks (with geo-locations) to a KML file -- that you can use offline. The tool is provided and the details are explained by Al Z e.g. in StackExchange Web Apps
As a general note: The way Googe has setup its Maps/Geo operations leads to a likely reality that Google will "never" provide good offline capabilities. Your proper solution comes from something that does. And that something is increasingly likely using OpenStreetMap. My personal recommendations for apps that can also (easily enough) handle your exported starred Google Maps locations are OsmAnd and Maverick. See OSM wiki for details and more options.
I tried saving map data from google maps onto my phone, not even trying to save marker layers, and found it unreliable at best. I eventually decided to invest in a satnav app that had maps stored locally on the phone, along with favourites etc. I have tried two, copilot (expensive and crashy but has the features of a true satnav, https://play.google.com/store/apps/details?id=com.alk.copilot.mapviewer&hl=en_GB) and Scout (much cheaper more reliable, better voice navigation but fewer features (no waypoints and limited avoid area/route support), https://play.google.com/store/apps/details?id=com.telenav.app.android.scout_us&hl=en).
If you specifically want google maps because of all its integration and search facilities etc then I'm stumped as to what to suggest.
Save locations for offline use
If you're already on a map that you want to save, you can save it without searching for a place.
You'll delete your saved offline maps if you clear your application data on your device. But you won't delete your saved offline maps if you sign out of the Google Maps app, delete your Search History, or delete your Maps history.
To make sure that your map has the most up-to-date information, your saved maps need to be updated at least once every 30 days. If you don’t update them, they’ll expire and be removed from your saved maps list.
Since you cannot search an offline map, save several smaller maps covering the same area. Name the map after the area.