The theory of special relativity says that our reference frame where they still exist is perfectly valid.

The reference frame in the middle of the cluster where they no longer exist is also valid.

No, a period of 5 years means it also gets close to Jupiter. This will destabilize any resonance it creates with Earth.

There may be a more complicated resonance with Earth, Mars, and Jupiter. But there is no reason to believe this would have a period of exactly 5 years.

The most dangerous radiation comes from outside the solar system and is called "galactic cosmic radiation". GCR is ionized hydrogen and helium atoms that are traveling very fast. It will destroy any DNA it hits, which is bad for humans.

There are four levels of GCR:

• On the ground. 100km of air gives very good protection. GCR is not a significant health threat.
• In low earth orbit. The earth's magnetic field gives some protection. We have measured increased cancer risk and cell damage from GCR in astronauts on the International Space Station.
• In the solar system. GCR is a significant threat to people traveling to other planets. Our current calculations are that most people will survive the trip, but some will get cancer and die.
• Outside the solar system. GCR is 10x higher outside the solar system. When you combine this with long travel times, an unshielded spaceship is a death trap. An interstellar spaceship would need a lot of radiation shielding.

Apparent brightness follows an inverse square law. This means an object 130,000 times farther away is only 1/130000² = 0.000000000059 times as bright.

There are other issues caused by the expansion of the universe. You can't see galaxies from 13 billion years ago with a telescope like Hubble, because the galaxies are moving so fast that they are redshifted out of the visible light range. JWST is special because it can see these galaxies in infrared.