I admit I have not tested using mod_mono in quite a while. I generally test with xsp2. I'm kind of busy with project work right now so I don't really have time at the moment to setup mod_mono and confirm the issues but it seems like Mono bugs. If you get different results under mod_mono than under xsp2 then I would definitely report that as a bug in the Mono bugzilla. I think the password issue still needs to be reported too if its still there in 2.4.
As far as errors in the log about missing tables, you will always see those errors after a new install because at first those tables don't exist, the error is logged but handled and then redirect to the /Setup/Default.aspx page runs the scripts to create the tables.
I'm not sure that using the Web.mono.config file is needed anymore, the primary difference is the use of 1.0 AJAX in the Web.mono.config vs use of 3.5 in the normal Web.config. Lately I have not been changing to the Web.mono.config file when I test, I just use the normal Web.config as the project references in our MonoDevelop solution now use 3.5 AJAX (System.Web.Extensions).
As far as compiling on Windows, I'm not sure thats going to work, you can try using the compiler directive MONO but I still think it may not work. I always compile the -for-mono release on Linux using MonoDevelop. Our MonoDevelop solution leaves out some files and adds some files not in the vs solution for compatibility. Some things like WebParts are not implemented in Mono and that stuff is left out.
I test primarily against Mono built from svn and I get the mojoportal code from our svn and open the mojoportal.mds (MonoDevelop Solution) and build that then test with xsp2. When I get some time I will setup mod_mono again.