over water 1400 feet deep,etc

We paddle toward Rubicon Point, over water 1,400 feet deep, one of the deeper parts of one of the nation's deepest lakes, though we're only a stone's throw from shore. My borrowed kayak is narrow, so my feet are boxed in, and my legs begin to cramp and spasm. My feet jab the rudder controls, and the kayak gets tippy. I dread being trapped upside-down again, so I stop paddling and brace myself for a plunge.

1 over water 1400 feet deep: Why don't he use "on"? Is that OK? Does he refer to his boat is floating on water?

On would be more standard usage. Over sounds like the kyak is above the water, but indeed, the boat is floating on the water.

2 one of the deeper parts of one of the nation's deepest lakes: I can't understand. Does the lake has two deeper parts?

It can have as many deeper parts as it wants. It can only have one deepest part.

3 cramp and spasm: Same meaning? Both refer to the syptoms similar to what football players face when they run a long time?

Not sure, so I won't guess.
4 the rudder controls: I'm not familiar with Kayak. What is the rudder control looks like? And what is that for?

There are foot pedels forward of the pilot which connect to the rudder at the rear of the kayak by means of pulleys and cables. Lake and ocean kayaks have rudders, by the way. White water kayaks do not.

5 tippy: What is tippy for a kayak? And when will the kayak be tippy?

All kayaks are tippy all the time. This means they can roll over and leave the pilot stuck in the seat while under water

6 trapped: Does the author refer to his experience of dropping into the water again?

Trapped is a result of tippy kayaks. See above

7 brace myself for a plunge: Can't imagine the action. Plunge: dropping into the water? for: get ready for? brace: with arms crossed befor one's chest?

An odd construction of words, but not uncommon. It means he is getting psychologically prepared to be trapped by that tippy kayak. I don't see how you could possibly figure this out from the wording, so go ahead and ask.

As to cramp and spasm: I think a cramp is more a prolonged muscle flex and a spasm can be a repetative flexing, like a tic. Maybe?