Hi
I will try to answer for you queries on each point. Moreover, I understand you are from .Net background and learning Dynamics Retail/Commerce. My recommendation will be understand Retail architecture before starting development, because this will be key important point to perform development. (I was also moved from .Net development to Retail and apart from architicture, understanding data flow there was no big challenge)
Answering point to point so refer your original questions for each respective question.
1. 'Testhost' project can be one of the client to test your customizations at initial stage but eventually if you have to consume the customizations in eCommerce / POS to verify. I do not use 'testhost' and will prefer to test customization directly on client. Take a note, Fiddler is the tool which will be very helpful to understand the data flow between different layer of Retail
2. It is Entity Framework and consumed by OData Service (retail server). Don't think about 'code first' or 'database first' in regards with retail, it is always parallel process which follow its own (Retail) architecture. You should create tables and entity classes, controller parallelly and test it. Follow the mentioned document or store hour project.
Understand the data storage mechanism 1. HQ and 2. Channel. You should again use fiddler to identify which layer of customization failing to retrieve and show the data.
3. 'AxDb' is exclusively for F&O but that's true for Prod and UAT environments because there is concept of scaling unit. For Dev environment AxDb hold both data HQ and channel and you can distinguish by schema. dbo is for F&O data objects, ax and crt are for channel data object, ext are for custom data objects.
4. ‘Synchronize Database’ and ‘Create Model’ options are for F&O database and code respectively. It doesn't have to do anything with CRT.
5. If you have created a table in channel database, that's not enough to show data on your pages. Create tables -> Populate data (CDX or user enter) -> Write CRT business logic -> create retail server OData API to expose the business logic -> then consume that to show data on your own pages in site builder.
Hope it gives you little more clarify. If it is please marked are answered so it can help others in community.
Regards,
Ram