Here's what I did with mine at the old house...

Mow at minimum 3 inches high. Maybe 4" during the summer. Fertilize on March 1st, June 1st and September 1st.

Water deeply (1 inch is 600 gallons per 1000 sqft) but you got a big yard so hope for rainfall instead of dry summer. I go as far as possible before having to water. When they are severely wilting but still green, it's time to water or they die by a bit. The longer you go, the more they die back.

That's about it. No widespread weeds because st aug was too thick for weeds to take over plus who cares about weeds? Just mow it and it looks fine. My parents had a big lawn so we just mowed. No raking. Just mulch mowed everything. Never was into watering lawn (garden/plant bed only).

For the bare patch, rye grass is often grown during the winter. They fizzle out when it gets very hot.

If your st aug have a thick purple reddish stolon, that's Floratam. Pretty tough cultivar for drought tolerance. If you don't have that, I suggest that you plug them in if you can find them. Maybe Lowe's or Home Depot or some of nursery stores have them??? Avoid Raleigh cultivar at all cost. Oh yeah, Floratam spreads out faster than any cultivars. Sapphire is the only one that can match that kind of speed but not sure about drought tolerance. It seemed pretty good for me. I don't know if it's available in Florida but you can get them at lawn plugs website.

Here is a link that might be useful: Lawn Plugs

I've got SO many weeds in my St. Augustine grass! The list includes oxalis, dollarweed, chickweed, sedges, hawksbeard, dayflower, matchweed, thistle, commelina, pliea, and spurge.
I don't know what a stolon is... but I see nothing purple about my grass?

Stolon is above ground runner that spreads out. If you don't see purple stolon, then it's not Floratam. Just common. Check with big box stores if they ever sell Floratam pieces. Just throw some pieces down on bare patches every few feet and they will fill in fast when weather warms up. http://www.plantanswers.com/grass.htm

Atrazine is what used on St augustine to kill weeds. If you can find end hose sprayer, use it if weeds bothers you that much but be careful of not to get it on trees, shrubs, etc. Don't saturate ground with it. Just enough on the leaves of weeds.

Here is a link that might be useful: atrazine

I guess mine is common then. I will definitely be looking for Floratam. I've got a lot of bare patches from a pool dig. Thanks!