Regarding a: It seems you only defined a terrain for the path, not for the grass around it. So for the terrain tiles in the top-right corner, you need to define a new terrain, which is the inverse of the path (so the outer edges on the 3x3, and the inner circle on the 2x2 tiles, and the 1x1 with just grass).
On drawing the path, you just draw atop of ‘nothing’, since your grass tile is not part of a terrain. The grey tiles only appear when the automapping occurs, and the terrain can’t find a match for a grass tile.
For b, you started out nicely, but indeed some randomness happens. When multiple options are available, the tool selects one at random. In your case, you only need a lava terrain of the left-most 3x3 and 2x2 tiles, instead of doing this on all four animation parts. And again here, you need to define a terrain for the stone floor as well, so the outer edges again.
Check out the 5th image here for terrain transition definitions: http://doc.mapeditor.org/manual/using-the-terrain-tool/
And last, no, there is no efficient way to change timings for animations. The best way I found is to go into the tileset-file, and ctrl+h to change all values in one go.
I hope this clears things up