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Too much nitrogen-rich fertilizer can discourage viburnums from blooming. You can counteract this by adding more phosphorus, like bone meal, to the soil around your shrub to encourage more blooms.

If your viburnum doesn't bloom, it could be because the species you have planted isn't appropriate for your growing zone. Too much fertilizer that is nitrogen-rich can also discourage viburnum from blooming. The age of your plant can be another factor. If the plant is too young, it might not be ready to bloom. They also need lots of sun. You can normally trim viburnum any time of the year without hurting the plant, but pruning may occasionally lessen the number of blooms. If you have not read it, this article will help:
https://www.gardeningknowhow.com/ornamental/shrubs/viburnum/viburnum-pruning.htm

This article will help with trimming them up a bit: https://www.gardeningknowhow.com/ornamental/shrubs/viburnum/viburnum-pruning.htm

This shrub is not listed as toxic on the ASPCA's poisonous plant list, and are only mildly toxic to humans. I found nothing about the leaves but the berries are apparently the toxic part of the shrubs. Birds enjoy eating these berries and are not harmful to them. If you are unsure about planting them, you could keep the berries trimmed off.

It may simply be going through some transplant shock from recent planting. It is possible that there are air pockets in the soil that are affecting the roots. I would step firmly on the root ball to help collapse any air pockets. Flood the area with water to help fill them in. Up its watering as well. It may also have a fungus disease, so I would treat the plant with a fungicide. This article may offer additional suggestions that you can try: https://www.gardeningknowhow.com/plant-problems/environmental/learn-how-to-avoid-and-repair-transplant-shock-in-plants.htm

This is typically caused by too little or too much water. Water the plant and then an hour or so later dig down a little ways near the roots. If the soil is still dry, the water may not be penetrating far enough. If water is pooling in the hole or the soil is sloppy, then drainage may be an issue and you should cut back on how much water the plant gets.

If the soil seems wet, but not sloppy, try to check the roots. Something may be attacking the roots of the plant, either a root rot or a pest.