Hi dear, I've been working in the fashion industry in the Philippines for around 3 years already.
To answer your question:
1. I have never heard of a modelling agency performing a medical exam. (After all, work is on a contractual basis, there is no need for a medical exam) And if it is indeed a medical exam, a talent manager is in NO POSITION to perform one and can only be performed by a doctor.
2. If you are a minor, you should always bring a guardian with you and the talent manager/agency should inform you this otherwise they would seem to have dodgy intentions. First of all, to be safe from harassment. 2nd of all, the agency CANNOT hire you without a guardian's consent. So kung pinapunta ka at hindi ka inadvisan na magdala ng guardian, malabo na yun. Obviously walang intent to hire you.
3. At any age in the industry, it is your personal right to choose how revealing you want yourself to be. It is your restrictions. So kung ayaw mo maghubad, they are not allowed to force you(unless you already agreed in the first place, signed a contract for a project and decided not to do it on the spot. Different case na yun). So kung VTR lang, ikaw ang bahala magsabi kung hanggan saan ang limit mo.
4. Also, most legit casting for revealing projects will immediately inform you in the msg they sent you kung maghuhubad ka (i.e. two-piece, topless, nude, etc.) Kung legit sila, sasabihin na nila sa invite palang. Mainly for the reason na ayaw nilang may mga susulpot tas sasabihin ayaw pala kasi hindi nila alam. It wastes the company's time.
Dear, will you tell me what agency that is and who is your contact person? =) Just so we are aware.
I, myself, have no personal encounters of sexual harassment in the industry(I'm a make-up artist and wardrobe stylist) but I have a lot of friends in modelling who experienced this when starting out.