Picket
You call it a picket.
A gate opens and closes, like a door. A fence partitions off pasture, crops, etc. and is not meant to be moved.
No if it is a foul ball or if it hits the fence and you catch it it does not matter you still can play it if it is not foul but if it is foul and you catch it when it hits the fence they just call it a strike. Actually - you CAN catch a ball off the fence. There is no rule against it, however it will NOT be counted as an out. The fence is part of the field just like the ground. Therefore, if it hits the fence in foul or fair territory, it is played the same as if it had hit the ground before you caught it.
No
No, "ence" is not a suffix in the word "fence." In this case, "fence" is a standalone word, and the letters "ence" are simply part of the word itself.
A RIPPLE in the wood
The switch.
Post.
The part of the fence that is yours typically extends from the boundary marker or property line to your side of the fence. If there are no clear markers, it's often understood that the fence belongs to the property owner whose side the fence faces. You might also want to check local property records or agreements with neighbors to clarify ownership. If in doubt, discussing it with your neighbor can help resolve any uncertainties.
A switch.
rail