Perhaps Xara LX is not feature complete in it's toolset yet, but the following works in the old Xara X (ie. the version before X1 and Xtreme):

For feathering, first create the shape you want as a "hole", feather and subtract it from a much larger shape. Then add that subtracted shape into a clipview of the outer bounds you want the shape to have.

For a more dynamic shadow than what the presets offer, simply create a new shape, set it to black with some transparency (linear if you want even) and apply some feathering. Voila, a shadow you have complete control over!

The centre of the gradient, ok... that's a stretch and now I'm going to give you the sort of tips I hate receiving in these forums (all long time members know their way around Xara like the back of their own hand, so whenever you ask for new tools, this is always the answer you get)... You can accomplish this with the blend shape tool. Place a source and a target shape, and blend between them. Then alter the color and feathering for each until you have reached the effect you want. (Yeah, I wouldn't be happy with that either, but you can expect a lot of those type of "helpful-but-not-really-what-i-wanted" answers on these forums.)

I also want more tools (ie. mesh fill) but somewhere you have to draw the line, I think.