Can the gyn doctor see if you have any STDs from looking at your vaginal area when he does the pelvic exam?

Sometimes. There are some std's that cause vaginal discharge that can be quite distinctive on examination but usually you need confirmatory tests by looking under a microscope or doing a lab test to be sure. Some std's dont have any signs or symptoms in girls and the only way to diagnose them is to do a routine screen. For example gonorrhea and chlamydia are tested routinely in girls under 25 due to risks.
Yes and No. Some stds can be seen on visual inspection, and that is an important part of the exam. However, others will need specialized tests, such as a pap smear (looking for sequelae of the std hpv), and others still can be tested for with urine and blood tests.
Some types. Warts (hpv active in the skin) are easy to see. Pubic lice can be seen. Other types of std's may require testing.