For surfaces, 'all-in-one' cleaning products like this this one work effectively. I usually spray the whole bathroom with it and then wipe it off with a cloth.
Hard Water Stains and Lime Scale
I use this product to remove hard water stains and lime scale from the sink. Spray it on, let it sit for some time, and then wipe it off with a cloth.
Vinegar or lemon juice can be used to remove lime scale by soaking a cloth in it and then wrapping it around the faucet. I got this cleaning vinegar for general cleaning purposes, but I haven't tried it on the faucet yet.
Inside of the Toilet
Ceramic Floors and Walls
While these tools can be useful, they are not perfect. Unlike an electric toothbrush that uses a back-and-forth motion, these tools operate in a circular motion. This requires additional effort to counteract the circular motion when you need to scrub in a back-and-forth manner.
I tried vinegar, but it didn't work well especially when the surfaces haven't been cleaned for a while. A solution that contains whitener compounds works best for this, and this product worked well in this case.
I got some ideas from this video: