So, if it is not an action reaction pair, then how is any force being
exerted by the table on the ball? Also, is the ball applying any force
on the table?
This is the crux of the issue.
There are two completely separate things happening here. One is gravity on the ball, the other is the ball on the table.
The first is Newton's Universal Gravitation. The force is due to mutual attraction. The ball is pulling on the Earth, and the Earth is pulling on the ball. The net result of these interactions is the the "earth part" is so much larger than the "ball part" that the later is best represented by zero. So to you, it looks like a net force downward equal to the mass of the ball.
Now when you have a non-zero force, what happens? Movement. But the ball is not moving. So where did it go?
Well that force on the ball is causing it to press into the table. The table responds by bending until the stress force caused by that bending is equal to the force put on it. Now you have two equal forces, so the motion stops. And since the ball is likely much lighter than the table's maximum weight capacity, the amount of bending is tiny to the point you can't see it.
Now of course the table is sitting on the floor, which similarily bends. And that floor is supported by walls, which are pushed down into the ground which compresses. And now you're at the Earth, so the force it put on the ball is ultimately balanced out.
Invariably when I see people confused in Newtonian examples it's because the experimental setup is being artificially limited by the question - in this case you ask what about the ball and the table and the earth. But if you look at the whole thing, you have earth->foundation->floor->table->ball->earth. So that 100g of mass in the ball that causes .1 N of force from the earth ultimately puts .1 of force on the earth and the cycle is closed. It's not the table that's balancing the force of the earth, it's (ultimately) the earth balancing the force of the earth.
Does that make sense?