2 quick questions

Should you add cool water before or after you pitch the yeast? Does it depend on the style? Or not at all?

Also, I brew on a 7 1/2 inch electric heating element on the the stove. I have a 7.5gal brew kettle that usually has about 4 1/2 gal of wort. With the lid off I get a boil but not a rolling boil. Should I leave the lid on to get it rolling or is any boil good enough?

Thanks!

You should add the cooled top-off water before the yeast in order to get the wort to the correct pitching temperature so that you don't kill your precious yeastie beasties (assuming you pre-boiled and cooled this top-off water to avoid an infection).......

Any boil is going to get the job done. A full rolling boil is best if possible (to avoid the much-debated possibility of off-flavors such as DMS).

Definitely leave the lid off. Putting a lid on there is just begging for a boil over and a very sticky mess (unless you are hovering over it, watching like a hawk).

Hope this helps......

-C

Leaving the lid off, lets the DMS escape... which is good

Never ever ever dump yeast into wort that hasn't been cooled to the correct temp. If you do and you're lucky enough that the heat doesn't kill the yeast you will get some nasty off flavors.