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It sounds like it may be a lack of nutrients. Add some slow release fertilizer to the container. It may also be a problem with water. Make sure that you are watering at least once a day if the temperatures go above 65F and twice a day when the temps are above 85F.

Pinching encourages bushier growth. Here is an article that you may find helpful: https://www.gardeningknowhow.com/garden-how-to/info/pinching-plant.htm

This link provides growing info for cherry tomatoes: https://www.gardeningknowhow.com/edible/vegetables/tomato/growing-cherry-tomatoes.htm

The following article should be of some help to you:
https://www.gardeningknowhow.com/edible/vegetables/tomato/growing-cherry-tomatoes.htm

The soil may be over dried, which actually causes it to repel water. Leave the hose on it for 15 minutes or so and just let the water run through the container to reyhdrate the water.

No, they cannot. It sounds like you have a mislabled plant or a fused fruit. There are varieties of tomatoes called stuffers that can look very similar to peppers, they are even hollow inside like peppers (and good for stuffing, hence the name stuffers).

There is also a condition where two or more blossoms fuse together and the fruit essentially grows as a siamese twin fruit. This can also give the tomato a pepper like shape.

Commonly referred to as hornworms--many of these insects can be easily removed by hand or with the use of soapy water sprays (mixture of liquid ivory soap, water and vegetable oil). Bacillus thuringiensis (Bt) can be sprayed on the plants. This insecticide attacks the digestive system of the insects but is not harmful to humans or plants, so using it on tomatoes is safe. Dusting tomato plants with red pepper will also help to deter the tomato worms.