Questions about PhD and research areas within Biomedical Engineering/Neuroscience

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Hello Gradcafe, I decided around a couple months ago that I'm going to continue my education through a PhD but have some questions that I haven't found specific answers that I need to settle in order to find focus in the PhD application and my current job. For context I have a B.S in Physics from Clarkson University and a M.S in Biomedical Engineering from Drexel University where in my graduate studies I specialized in neuroengineering. I have been in contact with my former University about my interests but was told there wouldn't be funding in my area for awhile so some Professors there have suggested to continue my education at another University where I now have my recommendations in order. I graduated with my Biomedical engineering degree in 2016 and got a local job as a support role of analyzing scientific data for quality of the raw data and won't be starting the PhD until 2018.

My first question is that I'm interested in specific research in the fields of neural engineering and computational neuroscience where the Professors/principal investigators that conduct this research tend be concentrated in different Departments based on the University. I'm specifically interested in a research lab that is focused on applying principles and gaining deeper understanding in the field of computational neuroscience in order to gain a better understanding of neural dysfunction in order to better treat neurological disorders, preferably using advanced techniques in signal processing, neuroimaging, and potentially data science. I noticed looking at schools other people are applying to in my field have both Biomedical Engineering and Neuroscience applications so is this normal? I couldn't find any specific information to this questions so I'm uncertain of the pros and cons considering I already have a Masters in Biomedical Engineering. Because of the interdisciplinary nature of my research interest both types of Departments could lead to the same type of research career so I need to answer this question.   

Also would it be wise to contact Professors on research if I have no specific research experience in their specific subject? I have two REU experiences and the specialization in neuroengineering from my graduate studies which was focused on getting people prepared for becoming apart of an University research group for further graduate studies. Because of this I do have research experience and coursework that was dedicated to reviewing scientific publications, making grant proposals, and creating innovative experiment designs but haven't actually conducted research in the specific area I'm interested in as a specialization. Once I narrow down my application pool I can start reviewing research of the Professors from the Universities but do have time constraints because of a full time job and other responsibilities. Would it also be advisable to be contacting different Departments to ask about funding in specific subfields such as neural engineering and computational neuroscience as that was a problem with my former University? 

Thank you for your time and look forward to the discussion!