Basic electric questions

Hi I am new so please bear with me...

When a caravan is plugged into an electric hook up, does it charge the lesiure battery? And if it does, does this require some intervention on the part of the caravaner or is it automatic?

Also, when off the mains and running off the leisure battery, do the ac sockets still work (i.e. via an inverter?) If not, is it straighforward to set this up?

Thanks in advance for any advice on this.