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Yes, but realize that it will compete for water and nutrients with the rose. I suggest planting them in the front of the container so the calibrachoa spills instead of climbing into the rose. If the rose is already snug in its container, it may be wise to pot it into a larger one so you don't have to disrupt rose roots when you put in the annual. When you remove the Calibrachoa, hold its place with a 3 inch potting cell, This will make it easier to plant next spring.

If the plant is growing well then try to get it some sun. Million bells is rated full sun to part shade which means it must have at least 4 hours of sun and preferably more to bloom well. Don't over-fertilize as this encourages lush green growth but fewer blooms. I would trim the plant back just a small amount all over if it is still a relatively small plant or by 1/4 to 1/3 if there are long bloom stems. Keeping the soil moist, not soggy, is perfect. Picture the difference between a sponge full of water (soggy) and one that has been wrung out (moist). In the shade, it may not need water daily, depending on weather and how much you give it each watering. Remember that many plants cease blooming in excessive heat and will pick up when more reasonable weather returns. https://www.gardeningknowhow.com/ornamental/flowers/million-bells/calibrachoa-million-bells.htm

Adding sphagnum peat moss helps acidify but there are commercial soil acidifiers at home stores. Here is an article on your choices: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/raise-acid-level-soil.htm
What I would do concerning drainage is a percolation test. It is a several step process to check drainage under the planting hole. Add enough water to fill the hole and let it drain. Once drained, add enough water to fill the hole again. If the water isn't gone in 24 hours, further amending is needed. https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/what-is-soil-conditioner.htm

This can be solved in many ways, and they methods will not harm your plants at all! My favorite methods for insect control as follows: Garlic oil, lavender oil, neem oil, rosemary oil, and on occasion, for tougher insects... cinnamon oil. You can mix one or more of these in a spray bottle with a few drops of each in warm water, and a spoonful of coconut oil.

This depends on the plant size and the hanging basket size that you have.

A common size of a hanging basket is 12 inches.
A common size of starter plants is in a 4 inch pot size.
I would plant 3 4 inch plants into a 12 inch hanging basket.

https://www.gardeningknowhow.com/ornamental/flowers/million-bells/calibrachoa-million-bells.htm