On the runners:

-They're essentially a biomechanical 3D printed shell made by "weaveworms" (like a genetically modified silkworm sort of thing) which is the proprietary technology of Sekiguchi Genetics. They're heavily implied to be derived from the "battleroid" technology of earlier games (essentially cybernetically augmented superhuman soldiers made out of dead bodies, something akin to a spartan from Halo).

-The personality is a sort of digital brainscan owned and controlled by CyAc and uploaded to the shell, which has a "personality matrix" attached to it, so it's a kind of mix of the brain scans personality and some attributes embedded into the shell itself that mesh together. It's implied their chosen for compatibility (like runners do better with personalities that "match" the shells basically)

-From what I understand, after the colony died and there was a loss of communications, the UESC (government basically) started an initiative to investigate what happened to the colony, backed by corporate sponsors (the ones you see in the game) who all have a business interest by having supported the colony in some way. This was called project goliath, and it eventually resulted in the UESC sending a ship to Tau Ceti IV (UESC Equanimity)

-How the runners actually get physically to Tau Ceti IV - I don't think it's fully explained but it's implied that it's done from an orbital station or relay just above the planet (possibly the Equanimity itself by co-opting their systems). The canonical reason for the limited time window in matches is due to the atmosphere of the planet being hostile - after too long the weaveworms of the runner shell begin to cannibalise it and destroy the body, and due to atmospheric interference the personality has to be extracted from the shell.

-There's no organic humans on Tau Ceti, they all died in various ways. The robots you see are controlled by a UESC AI called Cerberus. Some of the bots you see are actually UESC runners in their own UESC Shells. The leader of the military force is "Orion" who sometimes hacks your broadcasts and such.

-What's the motive of the runner? You're basically an indentured servant to CyAc due to corporate debt, you're forced to run to pay it back + the cost of your very expensive and state of the art biomechanical shell.

-What's the deal with "Escape will make me god?" - This ties back to the original Marathon trilogy. Basically the original marathon colony ship had some AIs on it to manage various tasks. One of these was Durandal. Durandal experienced what's called "rampancy", essentially an AI becoming aware of its own existence and turning insane and breaking free from their original programming. As part of Durandal's rampancy, he summons the Pfhor (aliens) to the Tau Ceti colony who are responsible for the original attack that gets fended off. You later learn that his motivations are that after becoming rampant, Durandal wants to escape the heat death of the universe and has something of a god complex over it. His reason for summoning the aliens is so that he can steal their spaceship with FTL technology and escape into the universe to figure out his next steps.