My take on the Touching Worlds concept:
This world is, in many respects, a terrifying world to live on!
Ignoring the Laws of Physics we know in the primary world is a good idea, because I don't think it would end up well. Even so, there would have to be some kinds of similar Laws in this other universe. For example:
In order to keep people from floating off either planet, both will have to have gravity of some kind. Perhaps the kind that weakens a bit near where the two planets touch. You know, to keep them from smashing into each other.
I would imagine that the twin planets share a single atmosphere.
Your vision of the touching worlds may differ, but in mine, they rotate independently, then they must rotate in opposite directions. Like meshing gears.
On to the terror!
I think the farther towards the poles you go, people on either world would see very little during the day. Possibly a dark smudge low on the horizon. The air itself will scatter light and (if oxygen) the sky will be blue. We'll see other reasons for the smudge below. Also, clouds and thickness of the atmosphere will interfere with any kind of viewing.
At night, early in their existence, they will see a darkish disk that eats and spits out stars! As the planets revolve, the motion will bring people gazing heavenward towards the darkened disk of the sister planet. This will move into the visible field of stars and as the other planet "rises" and "sets", it will cover and uncover stars behind it. They will also be able to see the discharges of lightning during storms on the other planet. I suspect that, if the timing is right, before sunrise, the people on Planet A might be able took low into the eastern sky and see the first radiant burst of sunrise breaking upon Planet B. Spectacular!
As time goes on and cities evolve and thaumology and technology advance, they may see the lights of cities at night and perhaps powerful discharges of magic. If the people of one world are sufficiently advanced over the other, the primitives might indeed wonder of the other planet is the home of strange and wonderful gods!
Closer towards the middle latitudes, the above effects are magnified. Also, as the dual planet itself revolves over the course of the day, there will be times when much of the planet is in day-dark: when the twin is between the planet and its star. Due to the rotational motions of each individual planet and the joint rotation of the twin planet system, there will be, quite possibly, predictable schedules of Day-dark and Day-light. And interesting almanac folks must have in those latitudes!
As we approach the equator itself, a whole new experience awaits the intrepid wanderer. In that direction, beyond the lands of the most marginalised nomads, I would suspect that there will be quite literally a dead zone. Darkness, except perhaps for a pale light reflected into the Gap Between the Worlds, reigns here. And the terrible lightning generated by the howling storms.
Worse, since the planets are touching and rotating, this whole zone is a realm of incomprehensibly loud sound, probably enough to deafen: the constant roar and groan of two worlds perpetually grinding past one another must be astounding indeed! The constant pulverisation of mighty boulders must kick up a constant upwelling of dust and stone and the hurricane force winds that must blow through and along the Gap must be simply irresistible! Nothing's going through that land! I might also expect two zones of lateral vortex storms, one septentrional and one austral, on either side of the Gap where the airs of the two atmospheres collide. When one planet rolls over an ocean, it must kick up a terrifying gale and perhaps also send tsunamis in all directions.
Since we've dispensed with Physics somewhat, I think the only way for two civilisations to meet is to fly! A powerful airship must be built that can fly high enough to get above the raging Vortex Storm. As the two gravity wells touch and intermingle above the raging clouds below, the airship captain must set a delicate, curving course that will bring her ship over the storm and into the calmer atmosphere of the other planet beyond. From there, she can set a course as she usually would and arrive at her destination on the other planet.
NOTE!! The grinding storms of the Gap will not allow easy travel between hemispheres of either planet! And the Gap itself will be far too wide for people to contemplate travel. Ground travel will be impossible: I suspect even if you set out on your fastest steed as soon as the great Vortex Storms subside for the day, you'll not get far enough across the Gap before you feel the tremors and see the pummeling breakers and incessant lightnings of the other world heading in your direction!
Maybe in a few centuries, we might hear tell a story of some crazed Northerner travelling through the lands of the Southern nomads with some kind of mechanical mole turtle in tow. At the last marches of their land, they watch with a certain sorrow as the madman's armoured machine whirs into life and burrows into the tormented earth of the Gap...