Good quality electric bikes are designed to handle wet weather, but they are more vulnerable to water ingress, so avoid storing them in wet/exposed areas and get them regularly serviced at your local dealer.
Depends on the brand. Most European brands will only supply motor power when the rider pedals. Smartmotion electric bikes vary between model – some have a throttle (like the MidCity, eCity, XCity, etc) Others do not, but have the ability to toggle between torque sensor mode or cadence mode (XCity, Hypersonic).
Not required for a modern lithium battery.
Firstly, any lithium battery must be treated with care as they do pose a fire risk. All major ebike brands use cell brands such as Panasonic, Samsung, etc, which greatly reduces fire risk. But fires can still occur (same for Lithium batteries in laptops, cell phones, etc). Charge your battery in a fire safe area,
Around 5 hours for a full charge, but a lithium battery can be topped up anytime too.
No. early ebikes had this feature, but it proved ineffective and the loss in efficiency uphill of a regen style motor depleted more battery energy than regen inputted when braking on downhill sections.