Welcome aboard
Sometimes the words used can seem 'off' to some people, anything like "What if any research has gone into those specific parts"
Not to say kiss up to all, but people do get labeled pretty quickly and with reason, because of the potential differences to the status quo from working devices.
I'll help out, though only have a couple of months experience with Bedini circuits specifically. Otherwise, about a year or so with other magnet motors and then from 2008 with R/C related CD-Rom drive based motors and their internals.
The distance is key for a few reasons. Much of anything to do with magnet motors is a Goldlocks principle...too near nothing, too far nothing, inbetween and there ya go.
Placing a coil too near to a magnet will induce a lot of drag. The core inside the coil will pull on the passing magnets and at best the system will run slower than optimum, at worst the whole thing will rattle and shake. If running just 1 coil, then the shaking and probable early failure of the bearings will be heightened.
If placed too far away, you may not even trigger the circuit into running.
The principle, as I understand it, is that a positive pulse is induced into the smaller winding. The other end of that coil connects to the negative supply of the battery. That positive pulse switches the transistor, via a small resistor (or ear of wheat bulb). The transistor now switched, then pulses the main drive coil and around we go.
As far as the diodes, they need to be able to handle the power going through them and be quick enough to not miss spikes. 1N4007 is a good one and plentiful.
I was forever stuck on such a simple to build circuit...wondering how on earth the transistor was able to switch. Best bet is to simply build and experiment.
Which transistor to use is not so much about current output ability. Pretty much any NPN power transistor with 2A and above output, will, inherently have voltage handling figures of 80V and above. The switching speed can be disregarded in terms of sheer speed, 4MHz is plenty for our wheels.
In the case of transistors that come from say a flyback on an old CRT PC monitor, you may find 1500V ratings. Those type don't need the neon across the Collector and Emitter. The popular TIP3055 is popular probably due to Radio Shack carrying them and that they only cost $1.89 a piece. Otherwise, it's really quite lowly in abilities. Better, I believe to head for the MJL21194 or something like the flyback ones. I've built a few wheels now and the only power transistors not to work well are Darlington types (D1414 was one recently). MOSFET's sort of work, but any power transistor will easily kick it into touch for ease of operation and to get a circuit to 'just work'.
To get a feel of what and how and why, salvaging is the least expensive method - a Freecycle advert for an old monitor will produce all the components required except the magnets, including the coil wire from the CRT neck
The magnets, depending on size of first wheel, can be salvaged from computer HDD's. For tiny wheels, you can use the little neo's found inside the laser assembly of CD-Rom drives (2 in each). Neo's from hard drives can be carefully cracked with sharp pliers to bring about useful dimensions.
It's not overunity. Arguably, overunity doesn't exist. What it does, is allow charging that will recondition a battery, rejuvenate an ailing one, bring about longer life from especially lead acids. The longer term usefulness of any battery is where positive effects from this sort of circuit are shown.
