I don't mean to disappoint you but planets are already charged - all bodies in space have a voltage that depends on their immediate environment to the degree that they interact with it through the interplanetary medium, which transfers charge to an extent.
Being isolated most of the time, they develop a potential compared to other objects due to the balances within their immediate environment being satisfied but by not having contact with other objects, their relative potential doesn't balance because their charges don't interact.
This is why in electronics and electrical engineering, two points cannot be compared in terms of their voltage, unless they share a point, usually ground. An example would be two batteries - while the voltage between their ends can be approximately the same (lets say 5V), if they're isolated from each other completely and you place a wire near them with a high enough voltage to overcome air resistance (say, 50 kV), against one there might be a spark, but not against the other, at the same distance (provided you kept the wire at a constant voltage). While this is unlikely to happen in the same room, due to the air balancing out charges through interaction and friction, it is possible to observe this difference experimentally. The ground in England is not the same ground as in Italy - but the voltage between the ends of batteries will be.
In much the same way, if two celestial objects where to pass close enough to each other to interact electrically, there would be huge lightning bolts. You don't see this often with asteroids because they don't often pass close enough to other objects and because given enough time in the same environment, their effective potential balances out.
But to answer the question, a planet can and does have a net charge - it's not something exotic, it would be exotic if it didn't.
Celestial objects are too far from each other to interact electrically this way, although they do interact through the interplanetary medium, albeit at a much smaller degree
Electricity and gravity don't interact the same way with matter. If a planet had a net charge, everything on it would share that net charge. Unless we're talking about a huge volcano (where events are violent enough to cause lightning), a thunderstorm, a tornado or an earthquake (where separations are again violent and there's a lot of friction involved), you wouldn't see much of a difference. Also magnetism is not electricity - they're related but not the same effect - unless the magnetic poles shifted dramatically (which does happen but never abruptly), you wouldn't notice much changing.
It would have as much an effect as it has now, on other bodies - the Sun controls most of what happens with charge within the solar system as it has the most powerful charge flows and emissions. It's hard to imagine a planet having a stronger effect on the charge of its surroundings than the star they orbit. Even if it were to happen, only the planet would face the consequences, not even moons.
Life would be no different - in fact, lightning is considered to be part of the necessary ingredients to get life and in the primordial Earth, we probably got tons of it all the time. With time, life adapts, the atmosphere stabilizes and things work out fine. The elements would also be the same, chemistry would be the same.
If the spacecraft entered the planet's environment too fast, it could get struck by lightning when it enters the higher (near space) layers of the atmosphere. But that would be easy to mitigate by just slowly adjusting its orbit until the potential is equalized, provided the pilot was prepared for this case.
Also, check Richard Tingle and supercat's comment's down below for more perspective.