Rather than relying on one server, is it possible to achieve high availability with two servers and no hardware load balancer?
Either Network Load Balancing and have SQL Server Express mirrored between the two servers (IIS would be on both servers too) or using something like Round Robin DNS and again mirrored databases between two servers?
Yes, if you use IIS 7, you can just install ARR (Application Request Routing http://www.iis.net/download/ApplicationRequestRouting ). To sync the content you can use Web Deploy to sync the content ( http://www.iis.net/download/WebDeploy ).
Syncing SQL Express is something that I would not be able to help, I would strongly recommend using a full SQL Server and just point both servers to it.