If the Earth as-is were moved to Venus's orbit (and Venus removed), would the Earth remain habitable, would it eventually turn into what Venus currently is, or would it turn into something else?
I'm mainly wondering which characteristics of Venus (hot, no magnetic shielding, etc) are the result of how it is composed compared to it's proximity to the sun.
Similar question: If Venus and Mars changed places, would we then have 3 habitable planets?
A planet's environment is a complex interplay of factors. If you dramatically change the insolation of a planet, it becomes very difficult to predict how the other factors which influence the planet's environment will respond.
Venus, for example, seems locked into its high-CO2 environment (which makes its surface hot) because its surface is too hot to allow for the formation of carbonates. Even if it had water (also needed for the formation of carbonates), it would be continuously boiled away from the surface.
All planets - Earth, Mars, and Venus included - have their temperatures influenced by their albedo. Albedos of planets are often strongly correlated with cloud cover. Cloud cover generally increases as a wet planet warms, reflecting more light. But atmospheric composition can overcome this balance, as in the case with Venus, which has a very high albedo but is still swelteringly hot on the surface.
Even if you get rid of the feedback factors like water and carbon dioxide, the planets have very different nitrogen levels - Venus at about 2 1/2 times that of Earth (enough to cause mild nitrogen narcosis on its own), and Mars almost nothing. Really, Mars in Venus's position would be in a terrible state - it's been so stripped of its atmosphere even as far from the sun as it is, it would be all the more stripped being much closer to the sun. Over geological timescales it'd become highly water stripped as well, as it'd be much easier for water to enter a gas phase, and the solar wind can very effectively strip water planets even as large as Venus, let alone Mars.
Venus in Mars' position would probably fare much better. But it's difficult to say exactly how much. Given that we can't say with great confidence exactly what set in motion the path that led to its current state today (thicker, more viscous lithosphere preventing crustal overturn? cause or consequence?), it's hard to say whether that would have happened had it been in Mars' orbit. One curiosity if you took today's Venus and moved it to Mars' position: you may well cause an atmospheric collapse to a supercritical state. It's been theorized that even in its current orbit that's happened before (temperature runs counter to the formation of supercritical fluids).
KarenRei's answer is very good as there is a significant degree of uncertainty, that said, I think the answer to this question is a clear no, the Earth would not be habitable at Venus' distance to the Sun. Not unless you're a waterbear living in a very deep cave.
Venus' average distance to the sun is .722 AU. Source. That means the surface of the sun is about 38.5% closer (A bit more than that since distance is measured to the center of the sun, not the surface) and because illumination drops by the square of the distance, Venus gets hit by 92% more solar energy per square meter than the Earth does.
It's thought that life on the Earth's surface could get difficult with just a small percent luminosity increase from the sun in as little as 150 million years or so and with a 10%-15% luminosity increase range (1 to 1.5 billion years), Earth could begin to have surface water vaporization, leading to a runaway greenhouse effect. Source. Some estimates say even sooner, 600-700 million years, or a 6-7% increase in luminosity.
These estimates are difficult to model and should be taken with a grain of salt, but if a 15% increase begins vaporizing lakes on land, and with water being a greenhouse gas, a 92% increase would be catastrophic, almost certainly leading to a very hot, Venus like surface temperature on Earth with a significant increase in atmospheric water vapor and perhaps Methane trapped below frozen tundra and CO2 from dying planets as well. I agree with KarenRei that there's considerable uncertainty in the outcome and cloud formation and albedo are difficult to predict, but Earth would still likely be hot enough to cook a pot-roast on the surface in that orbit. I don't see any way it wouldn't be, and possibly not enough to melt lead like the surface of Venus.
Perhaps, in the deep oceans (if the oceans survive, and I'm not sure they would), or in caves or permanently shaded caverns with access to underground water, some rugged life might survive.
As to Earth's magnetic field, it's not all that relevant to your question. Without a magnetic field, a planet is more likely to lose it's atmosphere, but that takes millions, if not tens or hundreds of millions of years. Venus has already been stripped of much of it's lighter gases. If you put Earth in Venus' orbit, that process would probably still happen, but it would take a long time and Earth's magnetic field would likely make the process slower.
The reason Earth has a magnetic field is somewhat complicated and there's many good threads on Earth's magnetic field in Earth Science Stack Exchange, but in a nutshell, Earth's solid inner core, liquid outer core and Earth's relatively fast rotation period are key factors. Earth's moon might play a role in maintaining it too. Earth's magnetic field wouldn't go away if it was in Venus's orbit. Venus lack of a magnetic field may be due to it's inner core not being solid and it could also be due to it's very slow rotation or a combination of both. But Venus' atmosphere creates an induced magnetic field, which helps it retain it's atmosphere. But that's only relevant to a planet's climate over the very long term as atmosphere gets stripped by the solar wind.
A 3rd consequence of Earth in Venus' orbit is the Moon would be much closer to an unstable orbital region. It would still probably remain in the Earth's orbit but it could be touch and go over thousands maybe millions of orbits, and the Moon would be significantly more perturbed and probably more eccentric at times and there's a chance Earth could lose the moon in this scenario, turning it into a dangerous near earth object that we would basically share an orbit with, and possibly crash into the Earth, or get tossed away by gravity assist.
