For consumers: no, not generally. Some markets have schemes to sell leftover solar power at real time prices, but I believe these are being phased out. Both grids and markets are by and large not set up yet for full two-way markets between consumers and producers.
I haven't heard much about that last part; like you said, it would be great if the market works such that on the margin a player can exploit that price to make a quick buck (by, e.g. rigging some kind of battery up before a storm that's coming and making bank off the arbitrage when the storm hits by emptying the battery back in to the grid). Now maybe the transaction costs or economies of scale or whatever make that infeasible-- if so too bad-- but it's worth remembering this is half the benefit of a market system.
If you sold the power back for real-time pricing you'd need a much larger system than your annual consumption. Net metering basically lets you sell the power back at a retail price, not a wholesale price.
I would also be curious in how the Texas case works. Especially if the grid is down, would it be able to accept the energy you are producing?
When the grid is down you can't sell power back. The whole system shuts down. Though if you have a whole house battery backup you can use that instead of the grid (if it is built for it - solar gets weird if you aren't using exactly as much power as you make so you need something to use or make up the difference).
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