More prominent. As dr. Mountcastle said, there may be a posssibility that running can slowly worsen varicose veins on your legs. Often runners have slender legs with very little subcutaneous tissue. As a result, the veins on runners' legs can be more visible and sometimes look like they are varicose but, in actuality, they are completely normal.
No. Varicose veins in the legs are caused by valvular disruption in the superfical veins, dvts, or deep vein insufficiency. ( their must be increased pressure in the veins for varicosities to form) running slowly has no effect. I do see alot of athelets get varicose veins in their calves however. So there may be some correlation between varicosites and atheletes but not running slowly.
No. This activity has no effect on the varicose veins. Wear support stockings and if concerned, see your pcp for advise on further options. Don't stop exercising unless it is just too uncomfortable.
VV and exercise. Varicose veins are due to malfunctioning (refluxing) valves of the saphenous system. Contraction of the calf muscles increases the venous return to reduce the venous hypertension and this is good for the veins. Running, however, because of the jarring and pounding of the legs on the ground can actually worsen varicose veins by the increased pressure on the valves. Non pounding exercise is best.