Which viburnum plicatum do you have?
I have two: Shasta and Summer Snowflake. They are woodland plants, so yours would benefit from some peat moss. Mix it with good gardening soil, and put it on top like you would put mulch on. You can do it again later in the summer and in the fall. You can then mulch on top of it too.
These viburnums don't really need to be fed- it all goes into the leaves, and not flowers then anyway. But,...they don't like the wind. Is your place windy?
The odd branch- no idea. Why don't you prune it?

They can also take several years until they finally bloom regulary and prolifically. I got so worried about mine a few years ago that I asked Walter Reeves about this and this is what he told me. He was right, a year later it bloomed beautifully, and has done so every year since.

I strongly advise not using peat moss. In addition to being a non renewable resource, peat moss cakes up on the surface and makes it very difficult for water to wet it again and enter the soil. Organic matter is always good for soil, but there are far better sources--wood chip mulch, straw, leaves, etc--than peat moss.

I would mulch it and try to keep it from drying out too much in the summer. They prefer to not be too dry.

I agree, in your zone, no peat moss. Peat moss and red clay are not a good combination. Instead, use lots of compost, lots of water, mulch, and some shade.