I'm familiar with some of the issues you describe, but they can usually be controlled with careful use of camera angles. I'm not a maths expert by any means and am still a 3D fractal noob, but I hope the following tips will help you...
1. Reducing the
FOVy value in the
Camera tab acts as a kind of secondary zoom, which can be used to get "up close" features, without causing slicing or moving the camera through the object.
2. I've not come across this myself in Mandelbulb 3D, but have occasionally experienced similar effects in older, 2D fractal software. Maybe someone with a better maths head can explain further; although again: a high FOVy value will give an effect a bit like a wide-angle lens and cause the centre of the image to "bulge out". Reducing the FOVy value *may* reduce some types of distortion.
3. Again, I would try reducing the FOVy value, to give a narrower field of view.
Manually adjusting the three Z values at the top right of the window can also help produce a "clean" image, free of cross sections.
The colour of cross-section of the sliced material can be altered to blend with its surroundings (although I can't remember how at this moment). Slicing *can* be used to great creative effect, to reveal additional structure, texture and detail within a fractal, which might otherwise remain unobserved. Have a look at the recent pictures by FF member haltenny for some examples of how slicing can be used as a feature.
If you really can't stand the slicing effect, then try Mandelbulber instead. It doesn't appear to produce slicing and has easier 3D navigation IMO - but be prepared for longer rendering times.
In the meantime, don't forget that both Mandelbulb 3D and Mandelbulber have been given FREE to the fractal art community by their creators. Jesse, Buddhi and others have donated many, many hours of their time FOR NOTHING except their love of fractals. 3D fractal software is still pretty new and still undergoing development; these are still early days and things can only continue to get better