I guess I need BASS, BASSASIO and BASSNET. Right?
You would need BASSASIO, and possibly BASS, depending on whether you need any of its features, eg. decoding. BASSASIO doesn't require BASS itself. The requirement of BASS.Net would depend on whether you're using .Net.
Do I still need VAC?
Yes, I think so, unless you create your own virtual soundcard driver to replace it. BASS does not provide a virtual soundcard driver itself.
Is there some Visual Basic 2010 sample code available, showing how to setup the required callback (marshalling - delegates)?
The BASS.Net package does includes some examples, but also see the BASS.Net documentation for code snippets, eg. the BASS_ASIO_ChannelEnable and ASIOPROC documentation shows how to setup an ASIO callback.
Is it simpler to write my application using PureBasic (instead of MS Visual Basic 2010), not needing the BASSNET wrapper?
Is it simpler and/or safer to write my application using MS C++ or MS C# because of finer or faster control about particular data types I may need (pointers) or any other reason?
Is it simpler and/or safer to write my application using another C compiler escaping from .NET, not needing the BASSNET wrapper?
If you need to do some DSP, then it may be better for performance to implement that in native code (eg. C++) rather than .Net, but overall it's probably best to just stick with whatever you are most comfortable using.
Question 5 :
In such signal chain, who is responsible for defining the final sampling frequency, the one that's used by the multichannel audio card?
When using ASIO output, the ASIO device will determine at what rate you need to provide sample data (via an ASIOPROC callback). The rate is available from BASS_ASIO_GetRate and can be set via BASS_ASIO_SetRate.
Question 6 :
In such signal chain, who is executing the resampling that's needed when playing a 48 kHz video soundtrack, and/or when playing a MP3 coming from a CD rip, and/or when playing a lossless file coming from a 24bit 96kHz audiophile vinyle rip ?
BASSASIO can handle the resampling (see BASS_ASIO_ChannelSetRate) or you can use the BASSmix add-on to do it.