Is there a MS Excel API/SDK? I just noticed a Excel plugin which was a dll
file. I am wondering whether it's possible for one to create his own
plugins for Excel and how to go about it?

I could possibly be way off base here, but I think that you need Microsoft
Visual Studio Tools for Office to create something like you're talking
about.

Also, is it possible to link in Excel with another application, say a 3rd
party program. So that Excel worksheets and cells correspond to values
stored in a 3rd party program's database.

If the Database is ODBC compatable (Many of them are) then it would
certainly be possible. It would take a little bit of VBA, but not much.
You would first have to setup the Database as an ODBC data source
(odbcad32.exe). Actually, I don't even think you have to do that, you just
have to create the database connection within your code.

Lydon Bergin
MCP, MOS