0.024" = 0.6mm which is plenty big enough. Even a low quality PCB supplier should be able to manage 10 thou.
If you want to autoroute a single sided PCB you should turn off the top layer in the router and set the bottom side to "direction *" - I think I have already said that earlier.
You should be able to route it without links. However, your ICs are too close together and 0.024 may be too wide to do that.
I haven't looked at the detail of the schematic, but it is drawn in a very confusing way. It is normal to orientate components all the same way round and have a logical signal flow (usually from left to right). Also, it is common to try to put positive voltages above negative voltages. You have half the components rotated through 90 degrees and signal flow is from the bottom left, up to the top & bock down again. You have NPN transistors which look "upside-down" even after you turn the paper round to read the legends.
Keith.