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The most common cause for this is that they are a type of Hydrangea macrophylla. These bloom on old growth, instead of new. If the growth is killed back in winter, then it can not develop old growth and will not flower often.

This article will help: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-not-blooming.htm

This article goes over the general differences between the two types of buds:
https://www.gardeningknowhow.com/garden-how-to/info/plant-bud-information.htm

You should keep them in pots with very little nutrients until they root. I recommend mixing a small amount of honey and an aspirin tab in some water and watering with that. It will help promote rooting. Keep them moist but not wet, or dry. Keeping them covered with plastic can help keep in moisture. Transplant when rooted, or after when it is time. Here is an article that will help: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-propagation.htm

Unlike nitrogen, phosphorus moves slowly through the soil. It can be added anytime since the effect is not immediate. It should be worked into the top 2 inches of soil so it doesn't run off in a heavy rain and pollute waterways. Where I live, soils are naturally high in phosphorus and only farmers and those growing in containers need to add a source of phosphorus. Too much phosphorus is not good for plant growth. You may want to test the soil every few years to guide use of amendments. Compost is also a decent source of phosphorus and is in a form that plants can absorb easily.

The roses shouldn't need it, but depending on the type of hydrangea, it may.

What I am concerned with is what seems to be a fungal infection. To be sure, add dolomitic lime and wettable sulfur to the soil around each affected plant. This will kill off the infection while reconditioning the soil as well.

Now, when to prune the hydrangea is a different story. This article will help: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm

This problem is not uncommon. The usual reason is improper pruning since it is very difficult to know whether those dead-looking stems really are dead. Some of them actually contain next year's blooms. Some hydrangeas bloom on stems formed the previous year; others form on current year growth. I suggest you not prune your shrub for 2 years until you can tell how your plant blooms. Plants also need consistent moisture. "Endless summer" and similar varieties need more sun than traditional hydrangeas which prefer morning sun or dappled, filtered light in afternoons. Use a long-acting fertilizer with the first number (N) is the same as or lower than the second number (P). Too much nitrogen stimulates leafy growth, not flowers. Several inches of compost may be sufficient. More info in these articles. https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-not-blooming.htm