I'm getting a serology test to check my immunity before i go on work placement. can i ask them to check for stds in the same test?

No: The work placement tests for communicable diseases that you can pass on by ordinary contact such as talking to people or even shaking hands. Sexually transmitted disease, for which std stands for, are not included in the category of ordinary contact. It would take considerable more contact to pick those up and thus, are generally not included in pre-employment panel.