Sharing a cup with someone who has herpes is an extremely low risk for contracting herpes. Quite honestly people shouldn't share cups to prevent the spreading of colds or flu.
Oral herpes is spread from kissing, or to the genitals via oral sex.
Do they oral herpes or cold sores the only way you can get it through sharing drinks is if they have an outbreak in thier mouth. If the have a cold sores which is different then genital herpes but is still herpes you can get cold sores by kissing them if they have one or sharing drinks but only if you can see the cold sore.
No. Genital herpes is an STD.