Can all players access the DLC levels?

The DLC levels (Schluesselschloss, Drachenfels, Karak Azgaraz, Stromdorf, Death on the Reik) can be accessed when invited by a Steam friend who owns the DLC (I have no experience with the console versions). I have recently seen many online posts claiming that ownership is only required for hosting.

Can solo players with only the base game play on the DLC maps? Do all lobbies show in the server browser? If not, what happens to vanilla-players when the server changes to a DLC map?

Short answer: No

Long answer:

• Vermintide doesn't use dedicated servers
• The person who created a lobby (aka the host) is the only person who can select the mission
• The host can only select missions that they own at difficulties that they have unlocked

If you're playing solo, you're the host and as such you can only select missions that you own. If you're viewing the lobby browser, you're just seeing games that another person is already hosting.