What are some of the major limitations of using SharePoint Foundation 2013, it's compatibility with Server 2012 Standard, and the limitations of SQL 2012 Express?
In terms of capacity and performance there are no limitations. SharePoint makes use of certain features in SQL Server Enterprise to enhance performance, such as table partitioning.
For SQL Server Express, database limitation is 10GB only. Some features which are not present in foundation:
Custom site definitions Site provisioning.
InfoPath forms service
Workflow Management-based workflows