Mono is C# only right now. There is mention of VB.Net support for a future version.
Mono doesn't have WinForms support right now. There is also mention of basic support for that in the next Mono version. WinForms is what you would use to create .NET Windows client apps.
And from the Oracle ADO.net Provider (what you would use to access the DB in .Net) status page: "Lots of missing functionality and bugs."
Why do you want to use Mono over the official MS .NET (besides the usual "MS made it so it must suck")?