If Venus and Mars changed places, would we then have 3 habitable planets? This is the supposition:
Venus is too hot, Mars is too cold. If they switched places then Solar energy would change to make both more Earth like. We might as well have had three instead of just one "Earth" in the Solar system, if the roulette of early planet formation had played out just a little bit different.

That's of course too simple. But wouldn't it help alot if it were the case from the beginning that Venus had had Mars' mass, and Mars had had Venus' mass? Or do other factors dominate mass and distance from the Sun?

Would Venus still have had a thick, but not too thick, atmosphere if it were at 1.5 AU, because it has mass enough to keep one, and wouldn't that have kept it warmer than Mars is today? Including flowing water on its surface under its atmospheric pressure?

Would a Mars at 0.7 AU have been warmer and maybe have had a passing atmosphere created from melting volatiles during a longer era in its history?
This is a very interesting question. Of course, as you noted, you have simplified things quite a bit; there are other factors besides temperature that affect habitability.

Regarding Venus, you probably know that Venus is extremely hot at its surface not just because it is closer to the Sun, but because it has a thick CO2 atmosphere and is warmed by the greenhouse effect. There are, in fact, two things about Venus that would prevent it from being habitable wherever you put it. One is the lack of a magnetosphere, which is necessary to prevent ionizing radiation (particularly from the solar wind) from reaching the planet's surface. The lack of a magnetosphere appears to be due to the lack of a geodynamo on Venus, which has to do with the structure of its core. Second, Venus appears to lack tectonic plates, which you may know are responsible for earthquakes here on Earth. Interestingly, tectonic plates play a major role in controlling the buildup of CO2 in the atmosphere (see here for details). Lacking tectonic plates, Venus is doomed to have a large CO2 atmosphere wherever you put it, which would not make it a nice place to live.

Mars, on the other hand, is a very different matter. It has both a magnetosphere (albeit it is very weak) and it likely has tectonic plates (although last I heard it is thought to only have two). One of the reasons that NASA has sent so many probes to Mars is that it was thought to be habitable at one point. It is thought that Mars's growth was stunted because of gravitation effects from Jupiter and Saturn. So, in another universe, Mars could have ended up very much like another Earth.