I have a solar charger, in the instructions it says not to.
You shouldn't be able to overload a solar battery charger. They will only provide the maximum current they can provide and then the voltage will drop. Similarly, if the car voltage is higher than the solar cell, it won't matter as they have a blocking diode in them to stop reverse current depleting the battery.
It shouldn't make much difference if the solar cell is connected when the engine is running, most people just leave them connected without any problems. The only reason I can think for advising of their disconnection is if they somehow confuse the charging circuitry of the car when its running, but I suspect it's not a real problem or there would be lots of dead cars as you will eventually fail to remove it anyway and the internet would be awash with warnings (which it isn't)..
yes, you can do drive around with the solar charger plugged in. But you should never leave your solar panel plugged in while you start your car, because the start motor will absorb any energy available, and that will overload the solar panels and can cause damage...
yep, but then you won't need the solar charger