The ATX grounds should be isolated, otherwise there would be short circuits between batteries. is it so? I'm not quite sure

If you were trying to make an actual BMS out of this, yes.. all of them would need to be electrically isolated to charge them while in series.  As it stands, I believe all the modules share the + leg directly.  Not sure, but it is definitely not isolated as this is a linear component and no inductors to be found.

However, that was not the intent here.  This was designed to be a charger which charges single cells (but 10 at a time), for the purpose of topping them off so I can discharge them and get a good reading.  That is all.

Hi Daren, Brian Benchoff noted the lack of reverse polarity protection in his blog write-up. How about some P-FETs and resistors to handle that? I hate to think of the consequences of an absent minded insertion (although I haven't actually looked into what they would be). 

Since the cells are all individual, the results would probably just be be one less working charging module.  There is an output N-fet of small size onboard.  Either that or the charger module itself is going to pop.  I'm guessing the onboard traces could handle about 5A before turning to vapor as well, so I think the effect will be self limiting in the worst case.

http://blog.deconinck.info/post/2017/12/22/18650-Battery-charger-reverse-polarity-protection

Has had a decent go at exploring the options. I like his idea of a buzzer to tell you that a cell is the wrong way around. Once you install protection it's hard to tell you have put it in wrong (apart from charging led colour) and coming back hours later to find a still-empty cell is probably so annoying that it makes the protection circuit worthwhile! 

you can also get these: http://www.ebay.com/i/263593791206, and just leave the top off, i made a little 3s li-ion battery out of one, they're awesome little powerbanks

I was trying to avoid charging the cells in parallel so a bad one can't pull down the entire cycle.  This charges each cell individually for that reason.  Used cells of unknown quality and all.  

I've had a couple cells that just sit there turning charge into heat, and never dropping below the cutoff threshold.  The charger has no idea if you have 1 or 20 cells in parallel so it just keeps delivering power.  Some got scary hot in the process, hence the active cooling now.  I'm doubling the heating now if I put a bad cell in, but at least it will fail all by itself.

That being said, your solution would make a good charger for lots of 'good' cells.  :)

Geez, you're getting a million great projects out of these cells. I loved the capacity tester ( #Minimalist Li-Ion Discharger/Capacity meter. ) and of course the spot welder ( #Minimalist Li-Ion Cell Welder ) is delicious -- can't believe it's that simple.

Great job all around.

Once you get that mountain board battery pulled together, how long do you think it will last? I longevity of salvaged cells just a matter of wise maintenance?

That is the one area I have thus far spent money, to save money. It has a proper BMS just because my son will be the one managing it, and I imagine running it completely dead would happen on the first run otherwise.  It was like $20 on Amazon.  I don't know how long the cells will last as they are all used, but I am within the proper rate of discharge with my 5p pack, so it should be a decent amount of time.  I'll be happy if I get a year out of them.  Given I probably saved $300 on the battery alone, I'll take what I can get.  I can always build another one now.  :)