Sql-server – Programmatically determine whether a database was shut down cleanly or whether it required crash recovery

Yes AG support multiple subnets as described here. Also make sure that your data provider supports MultiSubnetFailover .. .NET Framework 4 supports it.

To answer your question ...

IF you use .NET framework 4 or 3.5 then the provider will support it as described here.

Also, a good reference to SQL Server Multi-Subnet Clustering is well documented.

With legacy client libraries or third party data providers, you cannot use the MultiSubnetFailover parameter in your connection string. To help ensure that your client application works optimally with multi-subnet FCI in SQL Server 2012, try to adjust the connection timeout in the client connection string by 21 seconds for each additional IP address. This ensures that the client’s reconnection attempt does not timeout before it is able to cycle through all IP addresses in your multi-subnet FCI.

You can take if offline or open as a single user.

To take it offline adapt the followin script, original at sqlauthority

-- Create Test DB
CREATE DATABASE [myDB]
GO
-- Take the Database Offline
ALTER DATABASE [myDB] SET OFFLINE WITH
ROLLBACK IMMEDIATE
GO
-- Take the Database Online
ALTER DATABASE [myDB] SET ONLINE
GO
-- Clean up
DROP DATABASE [myDB]
GO

To make it available to a single user account original at sqlauthority:

ALTER DATABASE [YourDbName]
SET SINGLE_USER WITH ROLLBACK IMMEDIATE;