To answer your second question: distance is not a factor, but difficulty is. 'Walk' is the general, neutral term. 'Hike' suggests a walk that is quite strenuous, maybe uphill and over difficult terrain. The opposite of 'a hike' would be something like 'a stroll'. You can have a hike or a stroll in the countryside, but whereas the first is strenuous, the second is slow, easy and relaxed. Both could be described as 'a walk'. And, needless to say, your perception depends on your level of fitness - one person's 'hike' is another person's 'stroll'!

A walk can be anywhere. A hike is a walk in a natural area, like the woods or a mountain.