I left my Intex pool and went on vacation, now I have a green algae swamp

(See bottom of post for pool details)

Went on vacation, came back to a pool with green algae on the bottom. In a day it spread from being a small 2x2 patch to covering nearly the entire pool bottom. Also had some tiny sprouts of plant life (roots and two tear-drop-shaped leaves) floating around in there.

So yesterday we bought a brush and scrubbed it all off. Netted as much debris and plant sprouts as possible. Dumped in bleach (4 cups). We normally run the filter 24/7, so we continued that. This morning the pool is cloudy but no longer green. You can see the bottom. I changed the filter, even though it was not too bad.

I have the test kit that maxes out the chlorine measurement at 5-10ppm. I'm normally adding about 1 cup of bleach per day to get in the 3-5ppm range. As a weekly shock I use about 2.5 cups of bleach. I have no way to measure exactly how high this takes the chlorine. It measures in the 5-10ppm range, which is the max measurement the test kit can indicate. I have a packet of "guess strips" but yeah it's a big guess. Nearest pool store is an hour away, so I can't take in a water sample easily.

So this morning the chlorine was around 3-5ppm. I added another 2 cups of bleach. We do not have a vacuum, but I'm not seeing anything on the bottom of the pool. I normally net out all of the debris.

Here are my questions:
1. Do I just keep running the filter until it clears?
2. Should I keep the chlorine level in the shock range? How much do you suggest adding, in cups, as a guesstimate?
3. Would it be reasonably safe to let the kids in the cloudy pool today, not knowing the exact chlorine level? Probably not even close to the 30ppm that the Best Guess Chart says is harmless to naked swimmers, may harm suits.
4. Today the pH has spiked up in the 8.4 range. Maybe higher, as I don't have a test kit that will measure any higher. Do I need to do anything about the pH?

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The details:

12' x 36" Intex pool, approx 1500-1700 gallons
Intex 603 filter pump running 24/7, 530 GPH
Test kits: HTH 3-Way, HTH 6-Way

7/14/13 measurements (3 week old pool):
CYA 30
Alk 120-130
Hardness 120
pH 7.2 (has more recently crept up to the 7.4 range)

Have been using the BBB method since about day 3.