Turing platform is a new platform release concept introduced recently. The mail thread "Introducing the Carbon Platform Release Concept" on dev and architecture mailing lists explains this.
As you know, A WSO2 product = WSO2 Carbon + Set of features.
Your question is also about building from source. I know you have an idea about the WSO2 SVN structure and orbit, kernel and platform. You asked those questions :)
As I understand the ESB 4.8.0 Building from Source wiki page suggests that you should checkout relevant chunk release tag.
The release matrix has the information about the each chunk for a specific product.
For example, if you want to build ESB 4.8.0, you should checkout turing-chunk04 tag. To build API Manager 1.5.0, you should checkout turing-chunk02 tag.
Since the platform has all products, you must checkout relevant tag to get the released product.
The backward compatibility depends on each product. For example, the ESB 4.8.0 is not directly compatible with ESB 4.7.0 as the underlying Carbon is a major upgrade and there are user management changes. In such cases you need to migrate data. However the proxies may be compatible.
In general, any turing platform product is not directly backward compatible with a previous version of product with Carbon kernel version < 4.2.0.
Question: Are turing release chunks backward compatible? For example, would API Manager 1.5.0 that was released with chunk 2 also run on chunk 5?
AFAIU, your question is invalid. API Manager 1.5.0 is released under chunk02 and there is no API Manager release under chunk05. However API Manager 1.6.0 is released in Turing chunk 6. So you must checkout turing-chunk06 tag to build the API Manager 1.6.0.
I'm not sure API Manager 1.6.0 is compatible with API Manager 1.5.0. I'm not aware of the changes yet. However I can assure you that there are no changes in the user management and registry tables.
The important factors with Turing platform are that all products are based on Carbon 4.2.0 and there is only one P2 Repository. This means that any turing platform product can install features from a single Turing P2 repository.
I hope this helps to clear out your doubts.
Thanks!