You said, "I am aware the inherent danger with PDF."
Apparently I'm not. What is the danger you are referring to?
In response to your question...there are probably 100 "correct" answers. Per my normal mode of operation, here are a few rambling thoughts. I don't know anything about your medical clinic, but I thought I'd mention that I'm actually fairly impressed with the access to medical records that are available these days. My wife has had the same doctor for twenty years. She has several medical issues so besides her primary care physician, she has a urologist, a gastroenterologist, a gynecologist, a neurologist,...and a few more. The neat thing is that all of the doctors are referred by her primary, so they all report back to him. I can log on to his clinics website at any time. I can bring up notes/reports from any visit in the last five years, including test results, etc. This also allows me to check and make sure all of her prescription information is up to date. As you probably, know, the first thing they always ask at a medical appointment (or a trip to the hospital) is "Are you on any medications". I just pull out my phone, fire up the app, and provide whatever information is pertinent at the time. Because of this...I don't actually find it necessary to keep any other copy of medical records, except for I do keep her prescription list on my phone in a OneNote file as I use it weekly to fill her pill box and this list is what I use to verify the prescriptions on her chart. Over the years, I have found that I do a better job keeping that current than her Drs do.
None of that helps answer the question you asked.
1) I cannot think of any reason to convert this information to a Word doc. While I have, often, converted a .doc to a .pdf for archiving/storage, I have never converted a .pdf to a doc for storage. In fact, often .pdf's or parts of them cannot be "converted" to .doc files unless they are attached as an image, and I just don't see the point in that. Besides, that's a file format, not a storage method.
2) I see nothing wrong with storing the information on an external drive. In fact, if I wanted to store information like you have described, I would put it on a thumb drive and save it wherever was appropriate.
3) or 4) I'm not sure what a cloud mail service is, but I have nothing against cloud storage like OneDrive or Dropbox. Basically, as I described above, my wifes medical records are in cloud storage. (Technically, so are mine, but there is virtually nothing there. I get a CDL physical every two years, but this information isn't sent to anyone but the DOT. The easiest and cheapest way for me to do this is at an immediate care clinic, and I don't send it to any dr.)
5) I see nothing wrong with storing the information in your My Docs or any other folder on your system that you want to use. I don't see anything magical about one place vs another.
I'm not sure I truly answered your query, but you are welcome to my thoughts.