Some of this falls under scope of practice, which can vary state to state. Your question is not only about billing/coding but also legal and compliance. I would recommend obtaining official guidance from a consulting expert after doing your own research if it is not black and white. That being said, here are some of my experiences.
Most states allow NPs to practice independently and prescribe medications. "Testing" depends on the test. For example, NPs may not take x-rays, but they may read x-rays. NPs may perform and bill for E&M services. It is rare nowadays, but you may find an insurance or 2 that will not credential NPs.
The term APRN can be vague and is comprised of several different types of advanced practice nurses. NPs are one type of APRN. Other examples are CNM (midwives), CRNA (nurse anethetists) and CNS (clincal nurse specialists). What one APRN is allowed to do for scope of practice and billing can vary greatly based on the type of APRN. From my limited experience with CNS in my state, they cannot practice independently and there is little more they can do than an RN. I would imagine for the services you are looking for, CNM or CRNA are not relevant.
For states that require a collaborative supervisory agreement for NP or other CNS, an LCSW would not qualify.