I’ve walked the same route for a month and my body is still not used to it

Do you stretch them? If not, go to YouTube and find a good calf routine.

Also, maybe you should change your shoes. The wrong kind of shoes can really fuck up a person. A sturdy walking shoe is a good option.

Well, if that's all you ever do for exercise then it's probably normal.

Make sure you are getting enough salt in your diet

Something's wrong. You either need to stretch more or take it more slowly. It's normal to ache a bit but not feel burning pain.

This is offensive to people that can't walk.

Not normal. How steep or far is it?