two important questions

An individual trained in a procedure can do so in a physician's office at his/her direction, because they are doing so under the license of the physician. This is what medical assistants do, in general. As for the other procedure, I certainly wouldn't do something that I wasn't properly trained and certified to do. You might want to consult the policies and procedures manual of the unit in question and ask the education department of the facility about this.

I would have to just clarify that. No one can give meds unless licensed to do so. Doesn't matter if a physician trains you how to... if you are working for an MD but have no license that allows you to pass meds, and he says, hey I'll teach you how to run an IV so you can help me... Don't do it. You are then administering medication.

... of course as a nursing student, or in a radiology tech program you would be directed by your instructors on clinical site. But cannot practice what you have learned outside of your program.

You need an Xray Tech license to do xrays. I've seen people with Limited Xray License that could do simple ones like extremities but still needed formal training. In some states you can apply for an Xray License exemption if the clinic is in a rural area but it has to be many miles away from a licensed facility. Most states do allow MD's to shoot their own xrays but they can't delagate or train someone else to do it.

You need to report it immediately to the state if xrays are taken by someone not licensed. Not only can the patient be harmed but also the unlicensed tech.