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This article should help with that: https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm

The following article should be of some help to you:
https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm

Mushroom compost is suitable for most garden plants. To get the greatest results when using mushroom compost, thoroughly mix it in with the garden soil prior to planting or allow it to sit over winter and apply in spring.

The following articles should be of some help to you:
https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm
https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-winter-care-how-to-protect-hydrangeas-from-winter-cold-and-wind.htm

They will grow back fine, but you will most likely not see blooming this year. Next year it will bloom fine.

It is hard to say if they will survive in the new location. Most likely they will, but I would need to know the variety to say for certain. In terms of moving them, the 10 year old plant would probably not make the move, but the 4 year old plant might. You run the risk of losing the plants if they are large, as larger plants are more susceptible to transplant shock. I would recommend taking cuttings, regardless if you move them or not. That way if they die when moved, you will still have their offspring to plant. This article will help with that:
https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/hydrangea-propagation.htm