Players have left a few comments on my Harvest Moon Forever site as to areas on the Map that are locked at the start of the game as well as Mining.
If you go west past Lloyd's house, you will arrive at a large pile of boulders that prevents access to the area to the north.
Once Felix gives you a Horse, you will experience an Event wherein Wilbur will clear the path and you will gain access to a racecourse. You will be able to practice racing here as well as racing your horse here in the Horse Race.
If you attempt to enter the dark area behind the Waterfall, you will see a prompt:
There's a strange power here... but nothing seems to be happening right now.
In fact, in the second year, you will encounter a new Bachelor/Eligible Girl here in the second year.
As for Mining and Ores: You cannot gain access to a Mine, as far as I know. The Small Coins that you find in the river and on the ground can be used to create metals. Ore Stones can be found in the river. They contain Ores. Lloyd sells Ores at the Bazaar. Wonderfuls exist in this game as do 'Charms' which your Character can equip.
I am exploring this game with the rest of you... I could ask obtain answers, but I think it is more fun to try to discover a little by myself. Thanks to the players who helped with this information.