I've had a couple of electric bicycles. The first one had a removable battery, it actually has a slot for 2 batteries to get double the range. And yes, you could take em off and charge them inside. It had pedal assist mode, and a throttle for full electric mode. It would go about 15mph. And if the juice ran out, you could always pedal it like a regular bike. It was cool, only downside was the batteries needed to be charged at least once every 3 months. If you let them sit for too long without charging, the batteries would go bad and wouldnt hold a charge anymore. And those things were like $120 each.
My second electric bike (the one I still have now) is pretty cool. It's actually a foldable bike with small tires and a small frame. It can easily fit into a car trunk when folded, me and my friend actually fit two of them in his trunk. It goes about 15mph. If you go full electric on the throttle, you can get a range of about 10-15 miles. On pedal assist though, I got almost 25 miles one time. A couple of downsides with this bike though, the battery is not removable at all, so it has just the one battery. However, it doesn't seem to go bad like my other bike would from letting it sit for too long. I let it sit for a while, recently charged it and took it out, and it worked just fine, which was cool. But another downside of this bike, is that if the battery does run out, you can't really ride it like a regular bike. There's a crap load of resistance, it feels like your riding through thick grass. So you definitely don't wanna run out of juice on this particular bike.
So basically, each bike is a little different and will have its own features. Some are very expensive, and may even be worth it. But I paid around $400-$500 for each of the bikes I've had. Definitely fun and worth it.