Buy power specific outfit

I can only definitively answer part (1), and that answer is:

Yes, once you have explored a system you retain that information and it shows on the System Map for you.

I understand from the game forums that the first players to survey a system get more income from doing so than later players - but that later players do get some (presumably this data is confirmation of the earlier surveyors' findings).

I recall from memories of statements by the developers (can't cite, sorry) that in the released game, systems that have been explored and see a lot of player traffic will eventually have space stations built and come under faction control. I don't know whether the faction that players sell the data to has influence on the faction that moves into the system.

Your upgrades made your power demands exceed your available power when you deployed your hardpoints. When you're equipping a ship you can see what the power draw will be with hardpoints deployed and without hardpoints deployed. If your power utilization goes over the available power from your power plant, then the ship will shut down the lowest priority systems.

The first thing you can do is pay attention to your power when you're equipping your ship.

When outfitting, the lower right of the screen shows various stats. The "Retracted" power use is when your hardpoints aren't in use, the "deployed" power use is when your hardpoints are deployed, and the "available" is what your power plant can give you.

This particular screenshot shows me evaluating a weapons upgrade that would raise my hardpoints deployed power utilization just over my total available power. Note that the red color is just what's used when that stat goes up; you have to actually read the numbers to know that it's gone over the available power.

But that laser is awesome and I still want to use it! Can I still do that?

Yes. You need to pick some things to shut down when you deploy hardpoints. You'll still get a dire warning, but only things you decided were non-essential will get shut down.

In fact, even if you don't want to equip more stuff than you can fully power, it's a good idea to set your module priorities, since it's possible to take damage in combat that reduces your power capacity.

Use the 4 to switch to the Systems panel of your cockpit, use Q/E to switch to Modules, W/S to select a particular module, and A/D to change the priorities. I suggest putting your thrusters in the highest priority (1), and putting the Cargo Hatch, Frame Shift Drive, Discovery Scanner and anything else you only want to use while docked or in frame shift into the lowest priority.

In this example, you can see that I have the Cargo Hatch at the lowest priority (4), thrusters and a low-power-draw weapon at the highest priority (1), other things essential during combat (shields, power distribution, another weapon) at the second priority (2), and things that would be really nice to have, but I can do without for a while (kill warrant scanner and life support) at priority 3.

Note that the list is sorted by how much power each module draws (the percentage), and that there's a graph on the bottom that gives you a good idea how much power utilization is assigned to each priority level.

A note on life support: If your life support goes out, you have an emergency oxygen supply that you can use for a while. It's possible to buy a life support upgrade that gets you a longer emergency oxygen supply.

After a lot more practice with running too much stuff on too little power plant, here's how I'm setting my module priorities:

1. Anything required when running from a fight. Thrusters, shields, sensors, chaff launcher, heat sink launcher, shield booster, etc.
2. Anything required for engaging in combat: weapons, power distributor, etc.
3. Anything nice to have in combat: life support, kill warrant scanner, etc.
4. Frame Shift Drive. If I have to, I'll put shield cells here, too.
5. Anything that's only useful in supercruise or with hardpoints retracted: FSD interdictor, fuel scoop, cargo hatch, docking computer.

As long as my power plant can power the first 3 priorities, I'm fine. If it can't power down to priority 4, it just means I have to retract my hardpoints and wait an extra second before I can frameshift away. If I don't have power for shield cells and put them into priority 4, that's not too bad, since when I need shield cells I'm usually fleeing not shooting. If my power plant is damaged, the 1,2,3 ordering still helps. If I can't power priority 3 with hardpoints deployed, I can always go into the modules panel and shut down my most power hungry weapons while doing a warrant scan, and then turn the weapon back on once I've finished scanning.