Answer: The Endless Summer hydrangea is special in that it is able to bloom on both old and new growth. This means it blooms first from buds on branches that grew the year before and then blooms later in the summer and into fall on new growth of the season. It is better not to cut it back as this will eliminate the earlier blooms. However if the plant has suffered winter damage you may need to cut back dead stems or branches in the spring. (The plant will still bloom but beginning a bit later in the summer.) Be very patient and wait to be sure the branches are dead before pruning them off.
Unfortunately, based on your description I am not able to identify the begonia you have. There are hundreds of different begonia cultivars with interesting colored leaves. It should flower, though, if well cared for.
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