This is called a putting green. It can also be called a practice green.
On each hole, it's just the green. The practice putting area is called the putting green.
it is called a banana ball.
You'll need golf clubs, golf balls, tees, and a golf bag to put all of these in. Gloves and a hat are recommended. You'll need to focus on your swing and your short game (putting). You can practice your swing at a driving range and most golf courses have an area to practice putting (if not, mini putt is better than nothing).
It is called a sundowner round.
mini golf is basically putting practice with obstacles
The best ball for putting is one that is perfectly balanced, so it'll stay on line. But golf balls aren't really advertised in this way. And no golf ball is marketed as a ball for putting. Most golf balls are very good for putting, but the premium ball ranges will be softer.
That's called the green.