I think yes he must have BMS I don't think the vendor can be allowed to cell pack inside EV without one under EU/US rules. The battery should say its C-limit, maybe OP can upload image to forum.
I would return the bike. Because already the vendor showed you they are not interested, then when the bike has more problems you will be out of luck. Plus, the bike doesn't perform to how you need anyway.
Who cares if it's tiny? I don't think thats a good reason to downvote it. I personally like driving golf-carts and mini EVs.
I'd like to hear more about the engine vibrating... vibration should be an easy fix unless there are fundamental structural problems!
Those tubes can all be filled with 18650 or lipo batteries. Definitely no liquid. Must be battery-powered, using high current and low run-time. Just enough to get over the water so he doesn't mess it up. But really I want one of these and I hope he make the plans open and more people cooperate.
Could be a holiday, there are lots in China. More likely, the business has gone out of business. Could be a fly-by-nighter, or its just normal and you bought from a smaller trade company. What kit were you looking for?