Having surgery to repair a damaged hymen won't happen. Surgery is done typically only when it's needed due to the risks it carries, such as to infection, like if someone has cancer, to remove the lump to treat it.
Also, no, it's not possible for even the most highly experienced, qualified and skilled gynecologist to tell if a woman is a virgin or not. This was falsely believed for a while, the reason being because the hymen is known as 'the virgin's veil', since it supposedly stretches or tears the first time a woman has sex. Understand however, that the hymen can also be damaged from a woman or girl using some different forms of internal menstrual protection - like a tampon, menstrual sponge or menstrual cup - or from strenuous physical exercise - like horse riding or cycling - and also through masturbating. Also believe it or not, it's possible that some girls and women can have sex without the hymen being affected by it.
Hope this helps.