What is the best tempature to set the attic fan to come on at ?

Hi folks, I know that the issue of water in a basement has been covered many times and I really don't want to add to it but I couldn't find anything about my problem in the archives, so sorry. So I get water in my basement when the heavens open and the torenchal rains are unleashed, but only then. When it is a sustained heavy rain, in the area of 4" plus in a few hours. I'm not the only one, my neighbor to the right of me and the neighbor behind me have water problems, as well. My neighbor to the left, though, has a sump (he is the only one on the block) and hasn't had any problems. The sump neighbor is at the bottom of the hill on our street, I am second above him. My basement is a semi-finished walkout. Of course, it is the finished part that gets water. The room is 27' x 22' with a finished half bath. The water seems to come up through the settlement cracks in the slab and runs along those cracks to radiate from the center of the room. At first I thought it was a drain in the middle of the room that the previous owner said to have problems with. I sealed the drain completely after the first incident but have had water three times since. The gutters are in good shape and the down spouts run out a minimum of 6' for all, some up to ten feet. The grading around the house seems fine with nothing near the house that would trap any rainfall. There is a long planters box along the front porch, but this is drained and does not appear to be the problem. So I want to add a sump pump. In the unfinished part of the basement, by the furnace and hot water heater, is a square hole with black plastic cap next to the wall by the bathroom and about 18" from the wall along the back of the house. If I pull back the cap, the hole is about 18" x 18" square with about 4" of gravel on top of soil. Also, there is a pvc pipe just below the gravel that runs parallel to the back wall and halfway into the hole. I think this is a rough in for a shower to go with the bathroom that was not included when the previous owner did the basement. It looks sort of like this: ----------------------------------backwall | |bath|-[-] | | |____| hole | | | | x |F H | | drain |-----------------| | | F= Furnace | | H= H2O Heater | | ----------------| frontwall So, my question is this, Can I just dig down into this hole, put a sleeve and drop a sump pump in? Could I use what might be the drain for the shower rough in as the drain for the sump pump? Do I need to trench to the drain tile I am hoping is around the house and just 30" from the this hole through the wall? Sorry for the length but I wanted to be sure to cover everything. The help is appreciated. Thanks in advance. Drew in KC, MO.