Hi, (I'm the guy who made that alignment tool video)
Let me just say I've been dying for years for the Inkscape tiling dialog to get some much needed attention, and thank you Valerie (and everyone else) for fleshing out so much about this. Simply figuring out the dizzying requirements of this as a tool is huge. The fuse tiling mode is exciting!
Being able to "draw" out which tiles get rendered is good. It would be nice to use a tile pattern to fill areas, but until wallpaper groups are part of SVG patterns, how about the tracing acting like a lasso select, trace out a closed path and create enough tiles to fill? Drag out an open path would still just add tiles to whatever tile edges you cross, control-cross-over-edge remove the tile you were just in? For fuse mode, this could get quite interesting if your tile render area has holes (not simply-connected in math speak)!
I would strongly encourage live preview to be a part of this. Tilings are complicated enough, and being able to visualize on the fly is quite important. If dynamics adjustments are allowed, these then are simply previewed. Perhaps have a live preview toggle.
Skew is important at least for P1. With other groups, skew breaks the actual symmetry, unlike p1. A p1 example where skew is essential: http://www.tomlechner.com/randompics/skew.png
For dynamic adjustments, having a separate tool to do this (or combined in a distribute tool) sounds good, as long as it can still be accessed easily during the tiling phase. Jasper suggested a kind of keyframing dynamics? There is potential there! That way (as Valerie suggested), most things, like color, blur, opacity, size, offset position, can be adjusted with existing line style controls, then (perhaps selectively) grab a keyframe of the settings. For random jitter, maybe draw little wub wub marks near the tile, drag to make more or less random? Perhaps a toggle for having tile controls OR dynamics controls on the canvas (if they take up too much room to have both at once)?
If you allow stacking different dynamics adjustments, the hard part then is distinguishing on screen how the rather large number of possible adjustments map to the tiles. I have yet to hit on an adequate way to do this in my own alignment tool, but gradient style keyframing strips (applied by rows, columns, linear or elliptical fashion) might be the preferred direction!
So a toolbar could look like this with everything else on canvas: [fuse mode v] [tiling group v] [live preview toggle] [tile/dynamics control toggle]
Managing guide points could just be a matter of clicking on the cell outline, with a hover status message saying "double click to add point" or something? To be really clever, one could float representative icons strategically on the canvas, and allow changing by clicking the floating icons, or with a context menu. Then you don't need a toolbar at all!
The distinction between Plain/clip/fuse/fuse cut is only relevant when the original object extends outside the initial cell. In that light, not sure if the Clip and Fuse would be all that useful of modes. Plain and fuse-cut might do it from my point of view. If that is reasonable, then that could simply be an on-canvas toggle.
I don't see why radial tiling need be separate from path tiling. To set a radial tile as proposed, you need to edit the original path very carefully as to fit in the radial tiling cell. It might be easier just to adjust a common rectangular object, then warp into a wedge to fit a circle (or along path). Start, stop, and aligning on the path (or circle) could all be done (as with my align tool) by pushing around little controls. Sometimes, though, adjustments only within plus or minus 1% are not good enough! Something I'm toying with is when you click and/or move those little controls, there would be a "detail obsessed" toggle to hover a number nearby indicating the new value. Click on the hovering number to enter a new, more precise value.
-Tom
PS. and what about Penrose tilings?