1) a) Source code for modules is not always available on a source project level or as a source attachment in an artifact repository but as far as I know, source code for a commercial-only module can be requested via Alfresco Support as a paying customer
1) b) Details would have to be inquired via Alfresco Legal as license / subscription agreements for the commercial product are not publicly available. In general though it is highly unlikely that you would be allowed to modify the modules and still be within the confines of the support aspect of the subscription agreement. Most definitely you would not be allowed to distribute modified code. And in general, you should not need to modify the source - using extensions mechanisms will almost always allow you to achieve necessary customisations without all the hassle of checking legal conditions.
1) c) If you write new modules for the Alfresco platform, you can put them under any license you want. The Alfresco core (the open source bit of the product) is based on LGPL, and its conditions (or lack thereof) for linked software apply.
2) Virtually no differences with regards to core and API. Enterprise provides some added functionality typically only necessary in, well, "enterprise" scenarios, e.g. scalability (clustering, transformation), support of commercial databases, content encryption at rest, optional integration modules systems like SalesForce, Outlook, S3, yada, yada... The scope of most modules / functionalities is easily googleable / available on docs.alfresco.com.
3) Activiti as an open source project is primarily the core workflow engine library and, in the newer versions, a simple modeller application / the whole Activiti cloud bit. Alfresco Process Services has so far been a productised application built around the open source projects, again with added functionality, an enhanced modelling palette, support for commercial databases...
4) Contact Alfresco Sales to get additional support for your trial, including access to any modules you need to include in that trial to be able to make a purchasing decision. Those modules are not available for just anyone to willy nilly play with them - Alfresco wants to be involved in the process to make sure you are doing a proper trial and are not going to make a decision based on issues you encounter due to lack of knowledge about the product / guidance / support.
5) No differences regarding module installation.
6) Modules written for Community can generally be run without issue on Enterprise, since they are based on the common core. Modules written for Enterprise may not be compatible with Community, either technically or license-wise - it all depends on who has created the module in question, how much of Enterprise-specific code is referenced / depended upon, and what the business / legal terms of the module licenses are.