My sump pump freaks me out

Now I know I've already posted about the sump pump in the basement, back in March or April when it sprang a leak and there was water water everywhere. But I just feel the need to discuss it again. To start it off, I now have this weird thing known as a BASEMENT underneath my house. You know, where I can go down underground, look out tiny windows and see people's feet outside, and see all sorts of pipes and stuff that were hidden in my previous Texas house. But this sump pump is this weird hole with a cover back in one corner of the basement with a pipe going down into it.

Not only does this hole in general weird me out, when it rains (or soon afterward) and it's doing it's job you can actually hear the water dripping down into it. Ever since the leak this spring I now obsessively go check to make sure the dripping is actually in the hole and not on my basement floor (thank goodness no more problems on that front). And I get a little freaked out when I see the water belch out the pipe that extends to the street, especially when I notice that it looks like my house is the only one with the water coming out of it. We think it may be due in part to the new air conditioner. The humidity has caused a lot of moisture to come out of the AC drain pipe which I assume is going down into the sump pump. But it doesn't make the situation any less weird for me.