And on mobile, use Organic Maps. It downloads Open Street Map data so it works completely offline, no internet is required once you download whatever regions you need. There are monthly updates for the map data and the app is open source and ad-free.
OSM actually does have a website where you can freely browse the map, I’m not really sure what you are saying here. The main purpose of OSM is to provide data for other maps but openstreetmap.org is a fully functional map website
That’s because, like I said, the main purpose is to provide data for other maps and services, but saying an OSM map website doesn’t exist is very silly. I find OSM.org to work fine for me, there’s third party OSM mobile apps you can use