Black algae, DE & sand filter, proper brush for old concrete

Hello and thanks very much for this forum.
I'm brand-new to the forum and pretty new to the care of the pool at my house...please bear w/my basic Q's...

POOL SPECS ---FYI:
15-20yo (?) concrete pool
Approx 40,000 gal (?)***
SWCG: AquaRite electronic chlorine generator (just replaced the Cell in May 2014)
Pump: Pentair IntelliFlo VS + SVRS (run 8-9hrs/day at 1600rpm)
Filter: Triton fiberglass sand filter (sand replaced Spring 2013; pressure gauge @ top reads in 'green')
Solar-heated
Muriatic acid added approx 1-2x/wk to maintain pH level.
Salt level (per readout on generator box) usu ~3600.

The pool has black algae on the bottom (ie, not sides). I've been educating myself via various posts on this forum as to how to best keep it in check. It sounds like the most important factor is attention and diligence (in addition to educating myself). Coupled with reg (every day or two?) Cl & pH testing, brushing, and what I've recently realized (ugh): shocking it from time to time. I am wanting to get a better care-routine going.

I believe it was my ignorance re the following factors (& perhaps others) that caused the black algae to surge (there have been previous surges of the bl. algae while I've lived here, tho I was not in charge of pool maintenance at that time) :
1) needing higher Cl levels than what my home test-kit read as "optimal"
2) my pH got a bit too high w/out my immediate remediation earlier this summer
3) I decreased the pump rpm from 1750 to 1200 (electricity VERY expensive in Hawai'i) for a few months; now have it at 1600rpm.

I shocked the pool 2 days ago & of course pool looks much better (!). Sadly, I did not shock it *immediately* after brushing, rather within 24-48 hrs of a full scrub-down with stiff-plastic bristle brush.

Q: Can I use a metal-bristled brush on the bottom or is that too corrosive? It makes for a much easier scrub, but I don't want to further damage the surface of this old pool.

I feel I do have a reliable / trustworthy pool dealer where I have the water tested. Going there today to check levels. I am new to your forum and have not yet ordered the K-2006 test kit via Amazon that you encourage.

Q: I believe I read that it's advantageous to add a cup or two of a DE slurry into the skimmer basket to help clear the pool of scrubbed &/or shocked black algae 'heads'.... True?
If so, a few questions about this, please:
1) Can i use the DE that I already use for pest control (SAFER brand, sold at HD): "77.69%" silicon dioxide from DE" (they do NOT list the other, ~32% inactive ingredients on the packaging), or must I purchase pool-grade DE?
2) How much and how often?
3) Do I need to increase the pump speed when adding the DE?
4) Do I need to backwash more frequently - in general? --when adding DE? I currently only backwash only after vacuuming or if I've needed to drain water.

Thank you very much!

***Please, what is the correct formula for a good estimate of pool volume? I have heard "(10)(w)(d)(7.5)"

Hi:

I have recently had what I think was black algae on a shelf surface and my steps. What I found that really helped was I poured some shock granules onto the shelf surface in a small area 4' x 4' with the pool pump shut off and I let that shock sit on the shelf surface for about 15 to 20 minutes. I then used a hand stiff bristle brush and really went to work scrubbing the surface and after some hard scrubbing the surface came clean. Now just how would you do this for the bottom? I can only say that maybe filling a sock with shock and attach to your pool bush and scrub it along the bottom ?