Yes, you can easily do continuous multi channel acquisition.
Yes, a circular buffer is employed - you can set the circular buffer size to be whatever you believe is appropriate, but you must be able to read data out of the buffer fast enough to avoid a buffer overrun error.
If you are using a single data acquisition device, then there is only one scan clock so there can only be one analogue input process and the scan rate has to be the same for all channels (which you list). In your diagram you show two separate data acquisition loops - you cannot do this if you are using a single daq device (only one scan clock).
The buffer can be read at any rate and varying amount you like, as long as you read it often enough so that the buffer does not overrun. You read out of the buffer in scans (of your channel list) rather than channels.
Look at the LabVIEW "Examples" e.g. Examples>Hardware Input and Output>Traditional DAQ>Analog Input>Cont Acq&Graph(buffered).vi
I've used this sort of continuous multi-channel data acquisition quite successfully, to create an XY "oscilloscope" style display - it literally runs continuously, all day long.
Just one caution though: Windows PCs can, and do, run multiple applications and processes, many unseen - sometimes these tasks can hog the processor time, slowing down your LabVIEW application to the point where the DAQ buffering may inevitably overrun (unless you have a very large buffer, and can "catch up" again). In my application I just trap the occasional overrun error, and transparently restart the acquisition - this might not suit all applications (there would be data gaps/loss).
If you need anymore help, just ask.
Mark.