A refrigerator of some kind is a core component. There are a whole lot of ways to produce a refrigerator with relatively simple materials and power sources. Solar power (heat-wise) or plain old fire would work. As an added bonus, we could use the condenser to help keep food cool. There's more than one way to keep a room arid, if we can't use a condenser for some reason. If we can't find a cave, we'll have to build or dig.
We don't actually need tires. We want them, but they're not strictly necessary. If there's no rubber, we will have to use wooden wheels, possibly with tires made of on-hand materials. What works depends on a lot of things. If we do have rubber, though, we'll be able to make a whole shitload of useful things, not just tires. Which is why we're going to want to find rubber.
Survival in a primitive environment, especially one such as this, is going to be difficult, no doubt about that. But I don't expect a high death rate. Quite a few of us are going to have some... extra fat to survive on. And with the Leveling, none of us are going to be more physically impaired than the average human. We're not stupid, either. We have survivalists on board (though not as many as /k/, probably), and a lot of us (like myself) just plain find this kind of thing interesting, and happen to know a bit about it. Whether this will be enough to keep us alive depends on a lot of stuff we haven't worked out yet, like where we're starting, if all of us are starting in the same location, what the environment is ACTUALLY like, and on and on.
As for leadership, some charismatic asshole is going to Upper Left Blue us all into action. Then he will be shot, or possibly eaten by raptors. And then we'll decide things by rolling dice.