Tjena!

How do you make a EA shortcut for a DBMS-project? with correct connection params. 
As has been suggested, you can just save one out of EA. But it's actually quite simple to create a shortcut .EAP file manually, and in a deployment where you work with multiple projects and add new ones over time this often ends up being simpler.
Here's a template for a SQL Server-based repository which uses Windows credentials (which is unrelated to EA's user authentication, see earlier posts in this thread).
EAConnectString:#Window title# --- DBType=1;Connect=Provider=SQLOLEDB.1;
Integrated Security=SSPI;Persist Security Info=False;
Initial Catalog=#Database name#;Data Source=#DB server and port#;LazyLoad=1;Note that the split into three lines is just for clarity here. When EA creates a shortcut .EAP, it puts everything onto a single line and no whitespace after the semicolons. The hashes are there just to signify parameters you need to replace. In a real file, there are no hashes, no quotation marks or anything like that.
Most of what's in the file is plain ODBC, so things like the correct DBType value for a particular database server are defined by Microsoft. Only the very first and very last bits (window title and LazyLoad) are EA-specific.
#DB server and port#: Something like
MyServer,1433 for an SQL Server server.
#Database name#: The name of the database on the server. If you set up a DB connection manually, this is in the "Connection -- 3. Select the database on the server" dropdown.
#Window title#: This is what's shown in the window title. It's a good idea to make sure this is the same as the name of the file, otherwise it's confusing.
I usually impose a naming scheme where the #Window title# is set the same as the file name, and the file name is set to
Meaningful project name (database name). The "Meaningful project name" is something that makes sense to the modellers, and the databases are named EA001, EA002, etc which makes it easier for the DBAs. If the client wants one or more reusable asset repositories they're RAS01, RAS02, ...
FWIW, we name ALL shortcut files with a leading "@" to separate them from REAL .eap files.
That's a very good little practice there, hadn't thought of that. I'll steal that for next time.

Finally, set up the shared folder so that only the EA admins can write to it, or at least make the files read-only. Just for drulleförsäkring.
HTH,
/Uffe