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If the branches are dead, they can be pruned out any time.

Regular pruning should follow the appropriate pruning for the variety that you are growing.
The links below have more information.

https://www.gardeningknowhow.com/ornamental/shrubs/shgen/pruning-old-and-new-wood.htm

Here is a link to an article with a video that explains the process of how this is done. It is certainly something you can do yourself if you are up for a challenge!

http://mikesbackyardnursery.com/2014/04/how-to-grow-train-flowering-hydrangea-shrubs-into-tree-hydrangeas/

You will need to read the label and check the N-P-K number on the packaging.
The link below will refresh you on the fertilizer requirements of Hydrangea.

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/fertilizing-hydrangeas.htm

Your plants may have been burned by the fertilizer.

You an try washing the plant with a spray of water.
Fertilizer can burn the foliage and the roots. It can kill the plant.

You will need to wait and see how the plant progresses.

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/fertilizing-hydrangeas.htm

The old faded blossoms can be pruned off of your plant.

https://www.gardeningknowhow.com/ornamental/shrubs/hydrangea/prune-hydrangea-bushes-hydrangea-pruning-instructions.htm

I think this could be mites or Aphids.
This could be treated with Neem Oil.

https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm