There is a passage in Midrash Tanhuma: “Lest you say that the Holy One, blessed be He, needs light like a human being; after all, the sun that the Holy One, blessed be He, gave him is an offshoot of the supernal fire.”

I don’t know whether one can infer anything from here about how they conceived of the sun back then.

There’s an advertisement with Chef Haim Cohen making a pizza from dough and sauce and toppings and cheese, and afterward he “cooks” it in a car for half an hour with no electricity, no fire, no oven, and no gas—just there in the middle of the day. Is that permitted? On the Sabbath?

There’s this kind of box with aluminum-foil lining and ordinary glass on top, and inside the box they put a pot or a plate of food, which absorbs the sun’s rays and cooks and heats the food in the box. Is that halakhically permitted on the Sabbath?

What do we learn from the fact that it says, “You shall not kindle fire in any of your dwellings”? It could have just said, “You shall not kindle fire on the Sabbath day,” and that’s it.

Could I have inferred that if I didn’t kindle a fire but found a fire, then I’m allowed to use it?

Or

If I’m not in my own dwelling but in a gentile’s house on the Sabbath, then am I allowed to kindle fire on the Sabbath to cook food? Or only to heat it?

If we know the prohibition of kindling fire from the labor of the Tabernacle, why does the Torah add multiple mentions of kindling fire on the Sabbath? Isn’t that redundant?

Suppose I have an empty cup outside and it rains on the Sabbath—am I allowed to drink from it?

Is it permitted to sunbathe on the Sabbath, just to sit exposed in the sun? Under what conditions?

Moshe, hello.
If you want to study the laws of cooking with fire on the Sabbath, go to any Jewish law book. This is not the place for that. If you have a specific question (preferably not a simple informational one), you can raise it here.

Nonsense is always accepted as words of the fathers. But the fathers never saw an electric bulb, and for them every light was fire. Communication, for them, was a dove. And the earth was the center of the universe. So is there really any point arguing about things that today are empty? Honor to the fathers. Contempt for their descendants who pose as them.

How is this connected to the topic exactly?

I happened to come across this question by chance, and the book was lying at the corner of my eye on the edge of the shelf. I said, this is a sign, and the matter has come from God, etc., and out of love of holy things I will quote this story before the community in its own words (from the book translated into Hebrew), by the secret art of touch typing. And indeed, most of that book is nonsense, but when there is a fine point in it, we expound it publicly. And even these remarks are diluted with water.

(Surely You're Joking, Mr. Feynman, pp. 273–274)

One day two or three young rabbis came to me and said, “We understand that we can’t study to become rabbis in the modern world without knowing something about science, so we’d like to ask you a few questions.”
Of course, there are thousands of places where one can learn about science, and Columbia University was very close by, but I wanted to know what kind of questions interested them.
They said, “Well, for example, is electricity fire?”
“No,” I said, “but… what’s the problem?”
They said, “The Talmud says it is forbidden to kindle fire on the Sabbath, so our question is whether we can use electrical devices on the Sabbath.”
I was stunned. They weren’t interested in science at all! The only way science could affect their lives was if it supplied them with a way to interpret the Talmud better! They weren’t interested in the outside world, in natural phenomena; they were interested only in resolving some question raised by the Talmud.
[[[Skipping ahead. Here there is a section in which Feynman tried to challenge the idea of a “Sabbath gentile” on ethical grounds, arguing that you can’t dump on someone else something that is forbidden to you to do, and he says that those rabbinical students there “started twisting, turning, wriggling—I don’t remember how—and they got out of it! I thought I had come up with an original idea—ha! They had argued about it in the Talmud for generations! So they finished me off very easily—they got out of it with no trouble.”]]]
In the end I tried to assure the rabbinical students that the electric spark that worried them when they pressed the elevator buttons was not fire. I said, “Electricity is not fire. It is not a chemical process, like fire.”
“Really?” they said.
“Of course, there is electricity among the atoms of fire.”
“Aha!” they said.
“And in every other phenomenon that occurs in the world.”
I even suggested a practical solution for eliminating the spark. “If that’s what worries you, you can put a capacitor in parallel with the switch, so the electricity can flow and stop with no spark at all—anywhere.” But for some reason, they didn’t like that idea either.
It really was disappointing. There they were, going forward slowly in life, only in order to interpret the Talmud better. Imagine! In this modern age, people study in order to go out into society and do something—to become rabbis—and the only reason they think science might be interesting is because their ancient provincial problems from the Middle Ages have become a bit more complicated because of some new phenomena.

And inspired by the holiday, I’ll mention a saying that was constantly on the lips of one of the professors: “Any physics student who hasn’t read Feynman’s three lecture books has not fulfilled his obligation.” However, the later authorities of blessed memory ruled that nature has changed, and one may fulfill one’s obligation even with the books of David Morin, and so is the main practical halakhic ruling.