1. He is riding a horse now.

2. He is riding on a horse now.
(Which one is commonly used? Do we omit 'on' frequently?)

3. He is riding/taking a bike.
4. He is riding/taking a bus.
5. He is riding/taking a car.
6. He is riding/taking a train.
7. He is riding/taking a plane.
(Are they all the same? Are 'riding' and 'taking' interchangable in the sentences?)

We would more commonly say "he is riding a horse", not "on" a horse, but both are correct.

"riding" and "taking" are interchangeable, yes. We commonly say someone is riding IN a car, "taking" a train or a plane. We might say someone is riding IN a plane or a car, but it's correct the way you have phrased these sentences.

If one is riding a car, I have an image of one straddling the roof as one might straddle a horse or a bike. One rides in the car. The same with a train or plane. We do say we "take" the train, bus, or plane since they are public conveyances, so we "use" them or "take" them.

1. Both sentences "He is riding a horse now" and "He is riding on a horse now" are commonly used, but they have slightly different meanings.

- "He is riding a horse now" implies that he is currently seated on a horse and in the process of riding it.
- "He is riding on a horse now" suggests that he is riding something else, like a bicycle or a motorcycle, while being on top of a horse.

However, the use of "on" is not necessary in the first sentence, as the verb "ride" can be used without it. The decision to include or omit "on" depends on the specific context and how specific you want to be in your description.

2. The sentences 3 to 7 can be used interchangeably with either "riding" or "taking" when referring to various modes of transportation.

- "He is riding/taking a bike" means he is using a bicycle as his mode of transportation.
- "He is riding/taking a bus" implies he is using a bus for transportation.
- "He is riding/taking a car" indicates he is using a car to get around.
- "He is riding/taking a train" means he is using a train to travel.
- "He is riding/taking a plane" suggests he is using an airplane for transportation.

In these sentences, both "riding" and "taking" can be used interchangeably to express the action of using a specific mode of transportation. The choice between "riding" and "taking" mainly depends on personal preference and the local language conventions.