I've never heard of it called a pitcher lot or pitcher pen. We've always called ours bullpens.
Some of them are right next to a field and some of them are fenced off behind the outer end of the field.
As far as size, I'd say it needs to be at least 60 feet and 6 inches long but typically a few feet longer than that to allow for movement.
The maximum slope should be 10 inches.