Seems like some of the cells have failed and have reversed polarity due to using the wrong charger designed for a higher voltage battery.
They wouldn't reverse because of the charger. It happens because they are lower capacity than the rest, so were already low or empty before riding, then riding drove them below the BMS protect level and then below zero. Why the BMS didn't protect them...could be failed, could be poor design, etc.
But make sure they really are that low first....
I am not sure but non-sequential wiring seems unlikely. I will probably proceed with checking the individual cells. I see on Amazon or 18650batterystore there is a battery charger and tester. Would that give me information on cell health and what tools are there to test cell health?
If they actually went negative, don't bother--they wouldnt' be safe to recover. To go negative, they'd have to have been really low charge-capacity compared to the ones that haven't failed yet...and it's possible others are headed that way.
Repairing it would require getting all the tools to do the interconnects, etc., learning how to do them, getting matching cells for the type that's in there that you know are good, doing all the work to fix it, and that's all going to cost probably as much as a new pack...and it will only be as good as whatever the worst cells still in there are, so if any of *them* are close to aging out, etc., then you have to do taht work again for those, and so on.
To use most of the cell testers you'd have to disassemble the pack pretty completely, and then you need all the tools, parts, and knowhow to reassembled it, essentially building a whole new pack.
How can I know if a BMS is working or not? I have tried to use the correct charger but the light stays green, so does it mean that BMS is working because it has a feature preventing charging if it is lower than 29V ? If I replace the damaged cells with new ones, do you think the battery pack can be saved or will it have balance issues.
Since any new cells you use won't be identical in properties to the other cells, it will always require balancing (even if all the other cells are identical, which they almost certainly aren't). If the BMS has a balancer, then you just leave it on the charger long enough to rebalnce at the end of every charge (until the charger stops turning on and off, usually a few hours or more).
If the BMS doesn't have a balancer, then you'd have to manually balance it.
But it'd probably a good idea to replace the BMS anyway, if it let cells drop below LVC and actually go negative.
What is a normal difference between voltage levels to be considered as balanced vs unbalanced?
Balanced is zero difference between cells (0.0000000000v difference)

Anything else is unbalanced.
Some BMS will even prevent pack use or charge if the difference is greater than 0.1v. (some are programmable)
AC