On his birth planet, Krypton, gravity was much stronger than it is on Earth, so Kryptonians developed a physique that could resist its pull. When he's on Earth, Superman's physique can defy the planet's weaker pull easily, and that ability, enhanced by solar energy, allows him to fly.
As it turned out, all Kryptonians are born with a genetic bond to Krypton itself, which prevents them from leaving the planet. However, Jor-El was able to successfully remove the bond from his son's DNA, allowing Kal-El to safely travel all the way to Earth.
Kryptonians don't possess any powers on their home planet Krypton (although sometimes it was stated that they were capable of flying but lost this power due to overrelliance on their advanced technology), due to its red sun and natural higher gravity.
Why do Kryptonians have powers on Earth but not on Krypton?
Physiology and powers
In the first stories about Superman's origins, all Kryptonians possess on their homeworld the same powers Superman has on Earth. In later depictions, their abilities are attributed to the differences between Earth's gravity and that of Krypton and the different radiation of the stars they orbit.
It was also though his sheer willpower and determination that Zod eventually overcame his temporary weakness of overloaded senses within Earth's atmosphere, and swiftly mastered the power of flight.
This General Zod (born Avruiskin) is a Russian who was affected before his birth by his parents' exposure to Kryptonite radiation. As such, he is empowered by red sunlight and weakened by yellow, the opposite of Superman.
This General Zod is a Russian who was affected prior to his birth by Kryptonite radiation because he was the son of two cosmonauts whose ship was too close to Kal-El's rocketship. This Zod is unnaturally weak under a yellow sun, but superpowered under a red sun (the opposite of Superman).
Due to the success of living in a sustainable atmosphere with little to no complications, a Kryptonian's body can remain in the same physical state for as long as possible. This can enable them to live well into their hundreds to even thousands of years with every detail of their appearance remaining unchanged.
No, they can't in the most recent canon, because while outwardly they look the same, inwardly they are biologically different (IIRC, Subject 17 scanned Superman once and detected different internal organs).
Sexual reproduction was prohibited centuries before, so Kryptonian reproduction is achieved through use of the Genesis Chamber, which can grow a fetus from genetic material donated from two parents. The Chamber can also predict the child's eventual physical features, medical history, name, and occupation.
Half-human hybrids can be made in multiple ways, either through sexual reproduction, cloning, or through genetic engineering. The existence of hybrids proved that Kryptonian and human DNA could co-exist in one being.
In most retellings, Jor-El wanted Lara to accompany their son to Earth, but Lara refused, saying their son would have a better chance of reaching Earth without her extra weight. Kal-El's spaceship then took off, leaving Lara and Jor-El to perish.
The red star was called Roa and red star radiation surpasses all their superhuman abilities. They're no stronger than the average human on their home planet. The initial source of Superman's strength, speed and resiliancy was because Krypton had 1000 times Earth's gravity.
The air on Krypton was noxious, the radiation was intense, and the gravity would have flattened you like a space pancake. I imagine Krypton as a pressure cooker — a meaner, less habitable version of earth. Yet, Superman's ancestors survived and his family did just fine there — at least up until the planet exploded.
This means that once exposed to a yellow sun, Kryptonians will age normally up to their prime, but the aging process will slow down considerably when their bodies reach a peak level of maturity. They are not immortal per se, but they age so slowly that they may as well be.
All in all, most would agree that Superman is perpetually somewhere between his mid-20s and mid-30s, but seeing as he is essentially immortal, his age is practically irrelevant, anyway.
The species was rendered critically endangered after almost all Kryptonians died when their main civilization center on Krypton exploded due to the instability of the planet's radioactive core.
It took Superman years to absorb sufficient strength from the yellow sun. On the other hand, Supergirl gained her powers almost the moment she landed on Earth. It's clear she absorbs her solar powers even faster than Superman. Beyond that, Supergirl just doesn't hold back.
When it comes to Kryptonians, the only one who has arguably reached Superman's status is his cousin Supergirl. Superman's younger, but technically older, family member had a much more difficult path to master her powers while living under the shadow of her universally loved cousin.
Which version of Superman is immune to Kryptonite?
In this dark future, an older Man of Steel had grown impervious to kryptonite's radiation after years of living in a yellow sun solar system. The Golden Superman of DC One Million was at an even greater power level, having spent several decades within the sun itself.
The killing of Zod gave a reason for the character never to kill again. Superman falling to the ground and screaming afterward — I don't think that was originally in the script, but I wanted to show the pain he had.
Supergirl even initially dominated General Zod in some iterations of their fight. However, Zod's superior combat skills allowed him to adjust and gain the upper hand against Supergirl, killing her in each timeline. Nigh-Invulnerability: Supergirl's body is virtually indestructible.
One of the most dangerous menaces in the Marvel Universe, Thanos would put up a good fight against Zod but just couldn't defeat the Kryptonian. Thanos probably has Zod beaten in a few places when it comes to power levels but Zod is vastly stronger and faster than Thanos.
