In the USA...
Can blood be drawn on a patient without their consent if their proxy agrees and the tests are in the best interest of the patient (though not life or death) and the patient is actively refusing.
Well, you are presuambly talking about an incapacitated/incompetent patient as a competent person (and competence is presumed) has the right to refuse treatment. In a non-emergent or urgent situation it would not fall to a surrogate decision maker such as NOK to make decisions and may instead require guardianship or conservatorship (depending on the state). Even in those cases, no one is going to routine procedures on a patient who is refusing and where it would be dangerous to do so (for example the patient will assault you if you try to batter them - and it is battery). The patient still needs to ASSENT to treatment, even if they cannot consent. No surgeon in their right mind is going to take a patient to the OR kicking and screaming.
Also these things vary by state. Many states (for example MA) do not have a best interest standard and instead use a substituted judgement standard. In the substituted judgement standard the surrogate decision maker is not acting in the "best interests" but supposed to honor what the patient would have likely done if they were competent (which may be based on expressed wishes when competent). Plenty of competent people may refuse treatments, investigations etc, and it would be wrong to force an incompetent person to have such investigations if we know that were they competent they would have still refused such interventions.
Can IM psychiatric medication be administered to a nonviolent patient in the same circumstances?
It's not a question of violence but dangerousness to self or others. In an emergent situation you can administer medications to a patient if there is an imminent risk of harm to the patient or others (for example an escalatingly agitated and aggressive patient in the hospital). Otherwise one needs to get approval from the court typically. Civilly committed patients are no longer presumed to be incompetent (though they usually are), so being psychiatrically hospitalized does not take away one;s first amendment rights, and there is also the right of due process (i.e. an administrative hearing determining the patient is incompetent to refuse antipsychotics) as enshrined in the 14th amendment.
There is huge variation in laws regarding civil commitment, competency, guardianship/conservatorship, right to refuse treatment etc among the states, but the above parses out the main truisms. For children its more complex. Many states give parents alot of powers (to force interventions, hospitalization etc) on children, whereas others recognize that parents cannot (necessarily) be trusted. However the supreme court has previous ruled that absent abuse or neglect, parents should be given substantial weight in decisions for psychiatric hospitalization. In some states you cant even prescribe psychotropic drugs to consenting, competent, minors without parental approval (which causes problems when the parents are nuts and refuse to allow their children to get treatment)
