Yes, and it can be a pleasure, but the day of the week matters more than you would expect. Choose a village with a daily bus, then treat the summer extras as a bonus.
Because the land was divided up, the stone was already there and grazing animals needed keeping in. The long straight walls mostly date from Parliamentary enclosure, from the late 18th century into the 19th.
It is the custom of decorating wells and springs with large pictures made from flower petals pressed into wet clay. Villages across Derbyshire and the Peak put them up in turn, from spring to early autumn.
Pick the Lakes for high fells and water, the Dales for walled meadows and long quiet valleys, and the Peak if you want to arrive by train from Manchester or Sheffield with the least fuss.
Yes. A public footpath stays a public footpath when there is stock in the field. What changes is how you cross it, particularly with a dog or near calves.