some grammar fixes in docs/appcontext

I was reading the docs, and it seemed there were a few easy fixes to make. I tried never to change the meaning of a sentence.

I hope this is useful, I certainly don't mean to be insulting.

The changes are as follows:

* "in lack of" -> "for lack of"
* pillar's -> pillars
* ~~however~~
* a touch of cleanup to the "two ways" paragraph
* ~~on there~~
* "database connects" -> "database connections"