Often we are told he gets his powers from our sun, but he also flies interstellar distances so he is sometimes very far from our or any star.
If he does store energy from our sun, how long does this last? I think under a red sun, he loses his powers. If so, is this because even if he is "charged" from long exposure to our sun, the red sun neutralizes such powers?
This is a comic-book character so the answer to "how long does his power last in <situation>" isn't easy to answer. The short form is: as long as the writers need it to. He can go for days under a red sun in one episode/issue, then be disabled immediately when someone fills a room with "red star radiation" in the next. Such is the way of comic books, and Superman is no different.
In general, the writers tend to stick with the idea that Superman's cells are little capacitors that can store up the energy he gets from our sun, although there's no consistent explanation of just how that works. As long as he has access to sunlight his cells continue to charge up, and whenever he uses his many, many powers the stored energy is consumed.
The problem, with regard to your question at least, is that there's no simple way to gauge just how much energy he has stored. He could be running on fumes or maybe he just swallowed an entire sun (refer to DCeased) and thus has essentially unlimited power. This might explain why sometimes he can go for days under a red sun before he loses his power, while other times (sometimes within a few issues or episodes) he is rendered immediately powerless by Lex flooding a room with "red star radiation" or something.
It seems that some writers think that being near a red star suppresses Superman's abilities, while others think that he just can't gain any power from an old, tired sun. Different versions of Superman have different reactions to it, but most of the time the objective is to make Supe appear as powerful as possible.
So... if he fills the tank a little and uses his powers wisely, Superman could conceivably last for years. I mean, he once tanked the energy blast of a sentient galaxy and absorbed more energy than Cyborg could quantify. Ate a sun. Ate the anti-sun. Oh, and absorbed the energy of one of the 7 fragments of the Totality, the source of power for the entire DC multiverse. He could probably run for a few billion years or so on that one.
Some examples of this are below:
When Tyrell hits Superman with a blast of synthetic red sun energy he is stripped of his powers.
Source: Superman: Earth One #1
But it's not just the "precise frequency" of Krypton's sun that does it. Here's a much older example where Superman's power is totally removed under a red sun.
Source: Action Comics #300
And of course in War of the Supermen we have Lex shooting a missile through a wormhole to turn our sun red, instantly robbing all of the Kryptonians of their powers.
Source: Superman: War of the Supermen part 2
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But when Superman and Lex go to Apocalypse in "Imperius Lex" the light of the red sun doesn't stop him, he just can't draw energy from it. (I'll go find more if Valorum is still not satisfied.)
Source: Superman Vol 4 #35 (Probably, but I always mix these up.)
As for Supe's unlimited power absorption... there are several we could choose. But here, a few issues back from that last image, we have a sun-dipped Superman (he flew through a bunch of stars) punching the World Forger so hard he destroyed the multiverse the Forger was creating (the pretty field of lights and broken space windows in the image below). Let me repeat that: he punched a nascent multiverse out of existence.
Source: Justice League Vol 4 #25 - "The Sixth Dimension! Conclusion"
And let's not forget the time Superman Prime wandered the universe for a while, got bored, and spent 15,000 years sitting in the sun absorbing power so he'd have enough juice to take down Solaris. (DC One Million #4 if you're looking.) (And yes, I know, he used a GL ring to do the actual job.)
In the episode Solar Power from Superman: The Animated Series (1996), the sun is temporarily turned red by the villain of the episode.
Superman still had his powers. But the more time went by, and the weaker they grew. Eventually, he could no longer use his heat vision and had trouble carrying heavy weights.
Here's an excerpt of that episode, in which he has trouble saving Lois Lane, and then has trouble using his heat vision. Embedding has been disabled, so I included it as a link.
At the very end of the episode, after a face off against the villain who was responsible, you can see him quickly regaining his power when exposed to the yellow sun again.
One example that doesn’t involve a red sun was the aftermath of “The Final Night” crossover, from 1996. The sun got eaten, and came back, but Superman was not able to recharge his powers from the new sun. He slowly got weaker and weaker, over several months. While that was going on, DC was doing a crossover with Marvel, and used this to have a weakened Superman team up with Spider-Man to fight Venom.
Another very memorable story where Superman’s cells absorbed energy from the sun—too much, instead of too little—was in All-Star Superman. I’ll just post the panel. If anyone scrolling this far down the answers to a question about Supermman has not read All-Star Superman yet, you owe it to yourself to.
Superman has also sometimes lost the ability to absorb solar radiation after being drained by the Parasite. One variation on this were in season two of Superman & Lois, when Allie Allston (who has the same name as the female Parasite from the comics) put him in a coma, but was stopped from draining him to death, and he woke up weaker than an ordinary human, without superpowers and feeling sick. Another was in the late ’90s, when his cells overcharged to the point that he lost control of his powers, and being drained by Parasite cured him.
As of right now, yes, Superman absorbs and stores solar energy in his cells like a battery, and uses that energy when he uses his powers. Heat Vision uses the power the fastest - the relatively recent power the "Super Flare" lets him use virtually all his power in a single blast, rendering him powerless for A Period Of Time.
He depleted his power in his battle with Doomsday, which is why he was able to be beaten and killed(*) as his invulnerability weakened.
Part of the problem is that the rules have changed so many times over the years. The red sun thing was often shown as working like a light switch - red sun, no powers, yellow sun, immediate full power set. Now it's more of a gradual depletion as his powers are used.
The effect of Kryptonite has changed as well - now it affects him by driving the solar energy out of his cells, weakening him, replacing it with the Kryptonite radiation, which is toxic to him.
As others have said, the details and time frame of the effects of these changes tend to change from writer to writer, as the plot dictates.
(*) he got better.
