For a browser game you have two options - browser storage (either using System Save/Load, or LocalStorage plugin), or cloud storage. Browser storage may be lost if player clears browsing data, but for many simple games this is not a big issue, and it's much easier to implement.
System Save action saves everything, so yes, it may restore old level layout. You can try adding NoSave behavior to objects which you don't want to save, but this may not work very well in some games.
With LocalStorage you can save just the information you need - for example player stats, current level number, amount of gold etc.
If you want to use cloud storage, take a look at services like Playfab, Firebase etc. You will need to compose a block of data with information you wish to save, and send it to the server.
By the way, most of С2 manuals and tutorials are still relevant for C3, so don't discard them.