There is a bit of give in the opening width requirement with this kind of slide. Typically, in this specific case with the overall 25.4 mm gap requirement if you make the difference between the outside dimension of the drawer box and the internal dimension of the cabinet between 25+ to 26 mm you should be fine.
When fitting the full extension drawer runners do I need to make the carcase inside depth longer than the length of the runner?
Yes, 10-15 mm is adequate, unless the instructions that come with the slides say different. This give a bit of fat for making front to back depth adjustments, and for any shrinkage in cabinet depth if the cabinet sides are solid wood, and not man-made board. For an inset drawer front, for example, with an 18 mm front set back 2 mm from the front edge, and a 450 mm slide you need to allow for the drawer front thickness and setback, so the sum is 450 + 18 + 2 + 10 = 480 internal depth. If you allow 15 mm gap at the back the sum is 450 + 18 + 2 + 15 = 485. For an overlay drawer front exclude the drawer front thickness from the calculations, i.e., calculate slide length + 10 or 15 mm, whichever you choose.
How much of a gap is needed between the top of one drawer box and the bottom of the next drawer box
Aim for about 6- 8 mm to allow for vertical tweaking.
and also between bottom and top of carcase?
3- 4 mm, again for vertical adjustment.
You don't say, but I'm assuming you'll be making a drawer box and planting a front, and you're going for an inset drawer rather than overlay. In this case the front is made both long enough and wide enough to cover the drawer box, but you should aim for a gap of about 2 mm at both the sides, and horizontally between the fronts. This allows for the inevitable bit of flex side to side and vertically you get with this sort of slide.
If the drawer front is overlay you still need the horizontal gap between the fronts, but you may go for a full overlay or something like a 3/4 or 2/3 overlay at each side. I usually aim for about 3/4 or 7/8 overlay as I prefer to see the outer edge of the carcass rather than try to get perfect full side overlay, which is unachievable in my experience: there's always one or two drawer fronts that don't line up exactly, and if the ends are inset a bit from the carcase edge the discrepancy is less obvious. Slainte.
