I sometimes use the nut to hold the stem when replacing the tube and pumping up the tire. When I'm finished I throw it in my patch kit.
I always put the cap on the stem. Just something I've always done. I think it keeps the presta valve screwed closed and dirt out.
__________________
The Lord is merciful and gracious, slow to anger and abounding in steadfast love. - Psalm 103:8
I am a cyclist. I am not the fastest or the fittest. But I will get to where I'm going with a smile on my face.