I usually charge batteries when they are uninstalled (typically my riding mower battery over the winter); but is it OK to charge a car battery when it is installed in the car? One of my car's batteries was drained by an interior light that was left on, and I'm thinking of trickle-charging the battery while it is still in the car.

is it OK to charge a car battery when it is installed in the car?
Yes.

Yes. You can use a regular charger too.

Or you can just jump it and let it charge itself. You will not want to shut the car off for at least a few minutes so take a drive or let it idle.