> Do you have to be on a parabolic escape orbit in reference to the origin planet to perform the first HT burn?

The Hohmann transfer ∆v equations normally assume you aren't in orbit around another body. 

The following all assumes we're doing some sort of ["patched conic" approximation][1], where we define a [sphere of influence][2] for each body and pretend it's the only significant gravitational influence within the sphere. 

If you were on a parabolic escape, you'd leave the origin planet's sphere of influence at zero relative speed, and then you could execute the Hohmann, but in practice you combine the escape burn with the Hohmann ascent burn, which I believe is more efficient than doing two separate burns: you spend less time being dragged back by the origin planet because you're going faster than you would for parabolic escape alone. 

So the cost of the parabolic escape burn, plus the Hohmann, plus the destination capture burn (symmetrical with the parabolic escape), should be a reasonably close conservative estimate (overestimate) of the actual burn cost. Remember to add the origin planet's sphere of influence to the starting altitude for the Hohmann, and subtract the destination planet's SOI from the ending altitude; this assumes you leave each body in the most favorable direction. 

> What are the delta-v requirements for an escape burn from a circular orbit, and for a capture burn from an escape orbit? 

The escape and capture burns are symmetrical, and should be just the difference between circular orbit velocity and escape velocity from a given parking orbit altitude -- this one is a [slight underestimate if the burn isn't instantaneous][3], but since you're not trying to be very precise I think you can pretend that this neatly cancels out the overestimate on the other part. 

  [1]: https://en.wikipedia.org/wiki/Patched_conic_approximation
  [2]: https://en.wikipedia.org/wiki/Sphere_of_influence_(astrodynamics)
  [3]: https://en.wikipedia.org/wiki/Oberth_effect