One thing I've noticed is that there is a downvoting police, that goes around giving -1 to anything they don't like.
Good, the system works. We encourage people to downvote content they don't find useful.
It's the same with many answers. They have a plus score, and I found them useful; yet when I come back a few minutes later, they have gone to negative.
Apparently, other people didn't find said answers as useful as you did. It happens, you shouldn't lose sleep over it.
Some of these questions were valid, though they could have been written better. But is that enough reason to mark them down?
Yes. If you want to help those questions get upvoted, you could try fixing them. You can comment and ask for clarifications, or you can edit them. Or both.
At the end of the day, a downvote is just a signal to readers that there's something wrong with the question. If you agree those questions could have been written better, then I don't see what's your problem with people signalling just that.
Are the people of this site too eager to give downvotes? Is this a good practice to get more people into the community?
No, at least not in my experience. I'd say it's the opposite, really, this site has had a bit of a history with upvoting crap. But it's getting better.
Now, downvoting may scare some contributors away. However, we don't just want to get more people in this community. That's relatively easy. What we really want is to get people to stick around and become more and more active over time. Our main way of achieving that goal is to constantly provide quality content, and downvoting is one of our primary quality control tools. Thus, in the grand scheme of things, downvoting is a good thing.