What's your question? Ask

This article will give you some more pointers: https://extension.missouri.edu/p/g6970

They will turn red on their own and there is nothing you can do to speed up the process. If you find that they do not turn red at all, you may have holly berry midge, which burrows into the berries and prevents them from turning red. Here is more info: https://www.gardeningknowhow.com/ornamental/shrubs/holly/holly-berry-midge-pests.htm

It is unlikely, but not impossible that they might pollinate. It really depends on what varieties they are and the strains.

If you're thinking of the way some plants, like black walnut, are known to "poison" the area around them to inhibit the growth of other plants, the answer is no. Hollies are not known to be allelopathic; in addition, mums are known to be resistant to such chemicals. However, it is highly likely that the roots of the hollies are "sucking up" all the water, causing the mums to fail. This article has more information on this interesting phenomenon: https://www.gardeningknowhow.com/garden-how-to/info/allelopathic-plants.htm

Generally, these are hardy plants, requiring little, if any, winter care. However, in extreme situations, the shrubs can be wrapped. Here is an article on growing holly shrubs that you may find helpful: https://www.gardeningknowhow.com/ornamental/shrubs/holly/growing-holly-bushes.htm

Any pruning will encourage bushiness, and shaping is just a matter of pruning until the shape of the plant is pleasing. This article will help you: https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm