Do doors slow dwarves down

Infections can heal on their own, but not always. The best method is prevention, which means having soap in your hospital so the doctors clean their wounds (and hopefully prevent infection).

If your dwarves ever become "pale" it means that death from infection is imminent.

You hopefully have a burrow defined that encompasses your fortress interior, for sieges and whatnot? Try extending that burrow so it covers the current surface of the aquifer, but not the z-layer beneath, and set the civilian alert level to restrict to the burrow. With a little luck that will cause your dwarves to treat the freshly channeled-open hole as forbidden and avoid jumping down into it.