Hi Edward
I purchased the YGJ lithium ion battery charger and batteries in the first of your links. I was attracted by the rapid charge and "constant voltage".
It is early days yet - and I haven't given them a great deal of use - but they seem to do what it says on the tin. The one exception is the charger. It claims that the leds will turn from red to green once charging is complete. I find that they turn from red to a sort of orange/red (with a slight green edge when viewed obliquely). I reported this to YGJ who advised that I had a faulty charger and they immediately sent a new one. However, it behaves in exactly the same way so I wonder if this is just a "feature" of its operation.
Charging does appear to be fairly rapid - though detecting the change from red to orange/red is not as easy as if the change was a simple red to green!
When used on streaming internet radio (so wifi is in constant use too) I get at least 7 hours at a high volume. Usage time could be considerably longer but I have always missed the point when the batteries actually run out! The "constant voltage" is a bit of a double-edged sword - the display tends to show a fairly stable 6.00v - 6.07v during use and, unlike other batteries, the voltage does not reduce over time (which is precisely in line with what the manufacturer claims). However, when the batteries are exhausted, the BB1 will just suddenly go off. This means that whilst their is no deterioration in function as the batteries deplete, it also means that there is no clue as to how how much battery charge is left.
As far as buying additional batteries is concerned, on the Amazon web-page you quote, the Q&A (further down the page) suggests that the manufacturer plans to start selling batteries on their own within the next few months.
Hope this helps.