Yes, a battery should have a BMS which will monitor for overcharge, low voltage cutoff, and most will keep your cells in balance. (Many BMS boards sold on ebay don't have balance circuits, so novice DIY battery builders are building substandard batteries if they use those parts.) In addition, your ebike controller has its own low voltage shut off limit, often set higher than the battery's low voltage alarm.
In my opinion, the best way to use a spare battery is to run off the main battery and switch connectors to bring in the spare. The spare can be mounted on a cradle, if you have room, or carried in a bag. When I carry spares, I use bags.
I have put batteries in parallel, but only for smaller identical batteries where I wanted to add the current. You have to check that the two batteries are of equal voltage when connecting them. If I connect two that are a half volt apart, several amps of current flows as they equalize. This won't blow things up. However, several volts might smoke something, while a fully discharged battery connected to a fully charged one is probably disaster. Simplify your life and be safer. Don't connect in parallel.