Can SQLite support multiple users?
Yes SQLite can support multiple users at once. It does however lock the whole database when writing, so if you have lots of concurrent writes it is not the database you want (usually the time the database is locked is a few milliseconds - so for most uses this does not matter). But it is very well tested and very stable (and widely used) so you can trust it.
You may read this short document for information when to use SQLite and not: http://www.sqlite.org/whentouse.html
If concurrent writes are an issue, you may want to look at Berkeley DB. The SQL API is completely SQLite compatible. In fact, it incorporates the SQLite executor top of Berkeley DB's storage engine, which does support multiple concurrent write operations.
Yes.
From paragraph #5 in SQLite FAQ:
Multiple processes can have the same database open at the same time. Multiple processes can be doing a SELECT at the same time. But only one process can be making changes to the database at any moment in time, however.