IOS: Tapping Update in App Store just launches the app

There is no publicly available data on the actual iTunes App Store download counts (except for occasional special events such as the 25 billionth app download contest, and a few individual developer reports). The exact app download numbers are considered confidential information between Apple and each developer (perhaps because an individual's earnings could be so deduced). Each developer has access only to the counts for their own apps.

That said, a few developers do report some of their download numbers; and there are various estimations of the download distribution curve based on this evidence: for instance this blog post, and this academic paper, both from 2011, which may or may not be accurate. (Disclosure, the blog post is mine.)

As for part #4 of your question, the "on average" answer may not be relavant, as the app download distribution may be so skewed that almost no app has a download count that is anywhere close to the mean average, but mostly a lot more or a lot less. For instance, whatever the big mean average number is, there are some reports that most apps get downloaded less than once per day.

When this happens to me, I find it starts because a download was interrupted.

To correct, I find it easiest to use my computer to install the update, which corrects each app it updates.