Gradient colour not following path of curved line
When I go to colour the gradient after applying it to a thicker curved line a new shape is made and takes the colour and gradient that I chose. This shape appears to be connected by the same anchors as the curve but is just a straight line.
You're welcome :)
Based only on your example images, it appears your un-closed path has been given a gradient fill (second image) whereas it had a white fill in the first image. You can see that it's set that way by looking at the fill and stroke preview icons. In image1, the fill color square is set to white and the stroke color is set to a gradient.
You can test this by holding shift and pressing the X key, that will swap the fill and stroke color settings of the selected object.
Pressing the "/" key will remove either the stroke or fill color of the selected object (setting the color to "none"), depending on whether you have the fill or stroke selected in the preview. Swap them by pressing the X key or clicking on the opposite one to the current one on the preview. (the "current" one is the one displayed "in front of" the other on the preview)
If you remove the fill the extra gradient will disappear.