Yes, it's about getting more use from the battery before replacement.
That's not a good choice, IMO. It trades things we want (like long lifetime) for high current we can never use. Putting a Corvette engine in a Chevette and driving like an old man/lady. You can never use more than a tiny bit over two Amps.
The battery types you really want are the same ones used for laptops, which have a very similar power demand. The laptop and vape makers all use basically the same battery, they are not collectively stupid, I think it's wise to assume they know what they're doing. State of the art for such batteries is 2200 to 2600mAh in a few cases. Suitable batteries come with tabs welded on (meaning they're designed for pack duty). Welding (or rather having someone weld) tabs on other batteries or you is a second best I guess, soldering directly to them is to be avoided......even by experts. I get the ones I use from All-battery.com (who's site seems to be having troubles right now).
Yes, that's the protection PCB in the photo, in the Solo pack it's on the side. Boards on the top only work with some batteries, the compartment isn't all that tall, the highest capacity (biggest volume) ones will probably need the side board (All-battery can help you there too).
Yes, that's the common JST battery connector, but be careful on Solo the polarity is reversed. BTW I'm testing one of these $10 packs from China:
http://www.ebay.com/itm/7-4V-2200mA...ry-/190875389263?ssPageName=ADME:L:OU:US:1120
It's doing OK, I've been running it a lot (lots of that dummy runs). It seems about 2/3 or 3/4 the capacity of the factory battery despite their 2200 claim (go figure). I'm a little concerned it doesn't have the high temperature cut out, the Solo folks put it in for a reason I think (adding costs and a potential failure point), I think I'd recommend installing one before casual use.....again, All-battery is your friend.
Regards,
OF