So if my application has to retrieve/update multiple instances of SQL Server database, can I use self-servicing model or do I have to use Adapter model?

When you say "multiple instances" it means "multiple catalogs on the same servers" or "multiple servers"? Anyway, in short Adapter is the best scenario to front this scenario (multiple catalogs or multiple serves with the same schema).

I meant multiple servers. Can self-servicing be used in this scenario at all? Also what benefit adapter model provides over self-servicing?

selfservicing doesn't give you a way to connect to a server per-call. Adapter does, as you can pass a different connection string to an Adapter instance used solely in a single method. Selfservicing's connection string is always global (as it hides that from you as it serves itself )