Maybe. If you have a propensity for varicose veins from a heriditary standpoint it may make it worse to stand or even sit all day. The best advice is to wear compression stockings at work. This will give you the ability to prevent the formation of some varicose veins. See a vascular surgeon who specializes in venous disorders.
Yes and No. One of the main etiologic factors in the development of varicose veins is occupations or activities where an individual is standing or sitting for long periods of time. This is because it leads to an increase in venous pooling and subsequent venous pressure in the limbs, which can eventually cause the bulging, dilated varicosities. Standing in line isn't quite the same, unless for extended periods.
Not really. One study has shown that people who have to stand at work for more than 4 hours a day every day for 5 years will develop more vein trouble during that time than people who don't have to stand as much. These were people who had already been treated for varicose veins in the first place though. So they were people who had already inherited a tendency for having varicose veins as dr. Salartash said.