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You will need to water a newly planted shrub daily for the first two weeks, after that you can cut back.
Your plant is also stressed so it may have dropped it's blossoms to save energy.
I would not trim anything on the plant right now, just work on getting it well watered and adjusted to it's new garden location.
Here is a link that list the care needed.

https://www.gardeningknowhow.com/ornamental/shrubs/spirea/growing-spirea-shrubs.htm

I do not see these plants on the list of possible poisonous plant to dogs.
Here are a couple of links for you.

https://www.gardeningknowhow.com/plant-problems/environmental/plants-poisonous-to-dogs.htm
http://www.aspca.org/pet-care/animal-poison-control/dogs-plant-list

Actually, this is simply an average spacing between plants (or planting holes) and does not have to be exact. As long as you stay within this spacing minimum, the plants will be fine. I usually measure from plant to plant, though you can do it however you like. If you're more comfortable measuring from mid-hole to mid-hole, this is fine too.

This looks to be a Spirea variety. Gold Flame is one variety with this color patter, but there are several varieties with this color pattern.

https://www.gardeningknowhow.com/ornamental/shrubs/spirea/growing-spirea-shrubs.htm

Provided they share similar growing conditions, they should do fine together. The pink blooms of the spirea will actually stand out nicely amid the soft pink and white foliage of flamingo willow.

Yes, you can cut your spirea back to about six to eight inches from the ground. If it is a spring-blooming spirea you will most likely not see flowers this year. If it is an established plant and a summer-blooming one, then it should bloom by August or September. Now would normally be the time you'd trim back a summer-blooming spirea anyway.