would it be bad for my feet to walk in racing shoes?

Some people walk around in thin flip flops all day. If you are concerned about the shoes giving you trouble (or they actually do) try putting some kind of support insert in them to give you additional arch support or cushioning (whatever you need, there are various inserts to help with various issues). 

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There's no specific reason racing shoes would be a problem. Considering they are expensive most people wear them ONLY for racing, so they last longer. That doesn't mean they are bad to wear as an everyday "sneaker".

It is hard to say, given the information you provided.

They look like good running shoes. You should be able to walk or run in them * IF * they are a good match for your biomechanics. If they are a poor match, you might be injured whether you use them for walking or for running. That's true of any good running shoes.

It would help to know more about your heel pain, and what  happened to cause that injury. It could be the result of using shoes that do not match your biomechanics, or it could have another cause. 

It would help to know why they are the wrong shoes for you. I don't see they were designed specifically for racing. People who reviewed them classified them as trainers. I would be concerned if they were racing flats.

Update, based on update in the question:

Thanks for the update. 

If the Saucony shoes are the right size for you, and the arch support and stability features they have is a good match for your arches and pronation characteristics, you should be able to safely use them for walking, running, or both.

Additional update: Saucony classifies it as a neutral shoe. Neutral shoes are best for underpronators. Neutral shoes also typically work best for runners / walkers with high arches. If you have flat feet or overpronate, you should avoid neutral shoes. If you have average arches with average pronation, you might be able to use these shoes. But, they might also be a problem for you.

i would just try it and if it causes pain use another shoe

I can't imagine that being a problem unless you have particular problems with your feet in general. but in general, walking casually with a shoe designed for running instead of a "regular" shoe will not harm you