the Earth was in a polar orbit around the Sun?
If you took the Earth's current orbit and rotated it so that the Earth's orbit took it over the Sun's poles (with respect to the Sun's axis of rotation). The Earth's current orbit is approximately in the plane through the Sun's equator.
This is called orbital inclination. Earth's is about 7 degrees (to Sun's equator), dwarf planet Eris has an inclination of about 44 degrees (to the ecliptic)
Would the equator be perpendicular to where it is now?
That would depend on what events caused the planet to get into that orbit. Some planets don't have their axis of rotation aligned very closely to the axis of orbit.
Object Axial Tilt in degrees
The tilt is shown by the arrows through the various bodies in this diagram:
It is worth noting that the tilt (or "obliquity") isn't constant. Some planets vary a lot, Mars varies from 15 to 35 degrees and over tens of millions of years may have varied between 0 and 60 degrees. The obliquity of Mars is often referred to as being in a chaotic state.
As well as time zones?
Time zones are a reflection of the Earth's rotation and not it's orbit. They are also a political invention.