1. Did they effect your bird's initial home point registration?
Nope, coordinates are saved on the internal memory of the drone upon takeoff, and can only be manually changed to another location. Today's electronics are really strong against RF radiation, not even a 800W magnetron at close range would change a bit from the memory of a drone. You would need an RF injector literally touching the PCB to impact a modern chip.
2. Did they effect your GPS?
They could if they are powerful enough and are emitting on frequencies around 1.2Ghz, but I've never experienced it. On the other hand, towers are usually made from ferromagnetic metal that could interfere with the compass if you get too close.
3. Is there any accepted "safe" distance one should take off/fly from them (not from a collision concern but from a navigational or GPS concern)?
10 meters would be enough for the general antenna. RF power dissipates at a rate of the inverse square of the distance, so it goes down pretty quickly. The same for electric and magnetic fields of the tower. But of course, every pilot knows the location of some "death antennas" that kill the signal whenever you get around 50 meters of them, just stay away from those.
4. If flying by one, might there be a "preferred" distance to keep away when passing?
If you are long ranging, it's inevitable to pass near some antennas, and they'll interfere with the connection to some degree. You want to keep them as far as possible, 25-50m for optimal signal performance.
If you have connection problems, the easiest solutions are just to reduce the distance between you and the drone, keep the controller antennas pointed towards the drone, increase altitude or use the FCC mode if you are in a CE country.
Always search for a clear, unobstructed line of sight between you and the drone, and the connection will be perfect at any range, no matter what.