First of all, not everyone will agree with answers to a couple of your questions, but I’ll take a first shot at it:
“Any advice on how I can best help my dad in this proces?”
Since your Dad isn’t new to HAs, that helps. If he’s been wearing analog aids, he may have problems adjusting to digital aids. They sound different. Whichever hearing aid you eventually select, try to pick one with which your hearing specialist has lots of experience. This is really important. New digital aids are complex, and can be tricky to program well. Be patient. Ask lots of questions.
“Any experiences with this specific product?”
Use the search feature here, and look for threads dealing with specific makes and models in which you’re interested. I wear a pair of Phonak microEleva open fit BTE aids. So far, I’ve been very satisfied with them. Even the entry level or mid-range HAs have great capabilities. Check the experience of the person that will do the fitting (programming).
“Any products out there with the same or better functionality for my dad?”
Just about any of the newer digital instruments should be good, as long as your Dad’s loss is within the range of HA.
“Can one shop online for aids? If so, where are some good/reputable sites?”
This is a “hot button topic”. I’ve seen both extremes of satisfaction/dissatisfaction. I bought mine locally, so I could get local “face to face” support. One potential alternative is Costco, which will have much lower prices than a private business. You’ll be working with a certified Hearing Instrument Specialist" (HIS), not an Audiologist.
“Since he’s looking at Behind-The-Ear, does he need a proper fit by a doc?”
No. Either an Audiologist or certified Hearing Instrument Specialist (HIS) should be able to fit a BTE without any problems.
“What about Hearing Planet or Genesis? Are they to be avoided?”
No experience. See above comment about online purchases.
“Where can my dad go with his tests to try out more aids for himself?”
Just about any hearing aid provider. Most offer a 1-2 month trial period. If you don’t like it, bring it back and try another, or go someplace else. There may be a “restocking fee”. Get the details, and don’t let the trail period expire.
“What would you all do in my situation?”
Just exactly what you’re doing right now. Get all the information you can, then make an informed decision that fits YOUR needs.