I am a 37 - should I buy a 38 or 39 for snow & ice climbing
Women's size - you don't have much. Do you have snow shoes with inner boot. Do crampons fit on both? Which crampon suitable for Mt Elbrus and Mont Blanc?

I don't know how Scarpa fits (especially their female boots--I'm a guy), but I know that my normal shoe size is 41 or 41.5 yet all three pairs of my La Sportiva mountaineering boots are 42. This size isn't too big for my foot, but it gives me slightly more flexibility to use sock-layering systems which are a very good idea for extended outdoor excursions (espcially mountaineering). Are there no stores anywhere near you that sell Scarpa so that you could at least get an idea how that brand fits your foot? I don't know the temperature ranges found on those two mountains you listed. Black Diamond Sabretooth crampon is a great all-around step-in mountaineering crampon that can handle ice as well. The regular Black Diamond Contact Strap crampon is also very versatile and uses straps (no toe or heel bail required on the boots) in case you want to use it with non-mountaineering boots or even regular winter boots for non-technical terrain. As for double boots, those generally are unisex. Both La Sportiva and Scarpa sell multiple models of varying weight, warmth and performance. I have La Sportiva Spantiks which are amazingly light and warm but are ridiculously expensive and stiffer to walk in that a lot of double boots. I but I love them dearly.