another way to get a 3 px thick circle could be to draw the circle (own layer of course) with the marquee tool - fill it in the wanted line colour. Then go to SELECT > MODIFY > CONTRACT - 3 px ... this works well with small contractions - not so well with large numbers as the shape might suffer but then you can use SELECT > TRANSFORM SELECTION and pull at the corner points with ALT and SHIFT pressed to retain proportions and center.
If you want to delete portions of a stroke just use the marquee tool select what you don't need and push delete.