It is possible that a pap smear be done with STD testing automatically or do you need to consent to STD tests specifically?

Two separate things. A pap smear is a screening test for cervical cancer. Getting tested for stds involves sending separate tests. Doctors and patients often link these items together though so it is best to specifically ask what tests are being done and clarify what tests you would like or do not want.
Ask your doctor. Some doctors will automatically test their sexually active female patients for stds, others don't. If you would like an std test, make sure you discuss this with your doctor before the pap smear, so they can do both at once.However testing for hiv, hep c, hep b, & hpv serotypes are done with blood.
Depends on doc. Some doctors will automatically perform std checks on their patients, while others won't. If you would like an std check, ask your doctor to perform one before your pap smear to make sure they get the necessary equipment.
Yes and No. The same vial that holds the cells taken during a pap smear can be used to run gonorrhea chlamydia cultures.It should only be sent to the lab with your permission, however, not without asking your permission.