SQL Server Embedded Edition vs SQLite
Based on your question "What support is there for multiprocessing":


SQL Server CE and SQLLite are single-user DBs that work in your app and deployed as DLLs
SQL Server (Express and above) (and MySQL, Oracle, Postgres et) are server engines where you submit a request


Either you have proper multiprocessing or you don't: not much grey area in between. The rest of your questions don't matter because of this.

An as example, SQLLite locks tables locking so you don't have much concurrency even if it nominally supports multiple processes

Edit, about SQL Server CE from SO


"SQL Server CE in a multi user scenario - is this really, really stupid?"
"What is the number of maximum concurrent connections for Sql CE 3.5?"


It looks like SQL Server Express is recommended for multi process access