LJ - when you do the equal split are you splitting the 10 frame box into two 5 frame nucs?
Yes (or into two 10-frame boxes dummied-down to 5-frames). That way you keep roughly 50% of the workers, and by placing the 5-frame Nuc on the old stand you also get to keep the lion's share of the established foragers, maybe 90% or so. That's a lot of bees to have in one nuc box - which is then ideal for raising q/cells.
Why do you have to feed the queenless split?
Because making queens is more successful when there's a flow on. If there's a genuine flow taking place then they'll ignore any artificial feed, if there's not, they won't. So feed is kinda 'belt 'n' braces'.
Also how can I be sure they'll draw QCs from the eggs of my good queen not from the eggs of their original queen?
There are three details I didn't include, for fear of making the method sound complex. The first you've spotted (!). So - after 48 hrs, inspect ALL frames in the nuc for q/cells and remove any which have been started except for those on your chosen frame (which is best marked in some way - I use drawing pins/ thumb-tacks).
The second detail concerns the cells started on your chosen frame. I prefer to inspect after 48hrs rather than 24 because there's then more q/cell growth to make judgments with. If one cell should be *significantly* advanced compared to the others, that suggests it may have been started with a much older larva, and so I'd remove and bin it if there are plenty of cells on that comb, or if you're short of q/cells then cut it out as soon as it's capped and donate it to a colony as usual, but make a note to keep an eye on that colony for possible problems later. Many people say that bees never make a mistake when choosing larva, and they may well be right. But - 'belt and braces' again.
The third detail concerns the cutting out of q/cells. Standard practice is to cut out cells a day or two before expected emergence, but some people cut-out on the day of capping, or the day after. I've done both and they seem equally safe - providing you treat the q/cells with the utmost care. Early cut-outs certainly prevent the disaster which an early emergence can wreak.
Putting some kind of cage around advanced q/cells isn't very easy with 'wild' q/cells, which is where the Cupkit and similar cell-bar systems score over this type of technique.