Is this a good time and safe to Silk Road in the 2nd week April?

I think it will be windy and there might be sand storms. Maybe you could plan your tour a little later, middle May, perhaps.
One week is enough for the key sites along the silk road . You may refer to https://www.travelchinaguide.com/tour/silk_road/ to get some inspirations.
It's not a big problem for a lady to travel alone in downtown places, but it is better to be accompanied.