I see the Berner Oberland Pass is available at these websites:
https://www.swissrailways.com/en/buy-berner-oberland-pass
https://oev-shop.bls.ch/en/product/berner-oberland-pass?productID=1061
Which is legit? Or are they both legit?
Do I buy the HFC in SBB App? So when a conductor comes to check tickets, I will show the BO pass (as a PDF document) and the HFC in the SBB App?
Use the actual website: https://www.berneseoberlandpass.ch
When i used it a few years ago, I was able to have both passes on my iPhone. But carry a paper back up just in case. I think if i remember there was a Wallet app for one or maybe both.
The easiest place to purchase the pass is on Get Your Guide, type into your google browser, type into the "Find things to do search bar, the BO Switzerland Pass", you can select what type of switzerland pass you want from there and for how many days ( the price is the same in USD that it is on the SBB websites in CHF) I have used both in the past and found the Get Your Guide to be a lot more user friendly, and also easier to cancel or change should you need to (I believe its refundable up to three days before) :).
The second link you provided, the BLS link, is a good option since the BO pass is a product of the BLS company. BLS operates many of the regional trains included in the pass and runs the boats on Lake Thun and Lake Brienz.
The link shared by @bimmerboyd is excellent, as it allows you to buy directly from the seller and provides all the information you need regarding the pass. You will see that the BO Pass website shares a link with the BLS as a place to purchase the ticket, linking the two together.
I would recommend either of these two options.
Yes, when you show your tickets you show the BLS pass and the HFC.
Always buy direct from the company who performs the service. The BO pass website for the pass. SBB.ch/en for any other train tickets or half fare card you need.
Always buy direct from the company who performs the service.
Exactly. Which is why you can also purchase the BO Pass from BLS AG. It is their product, as I stated above.
Looks like BLS (the second link I posted) is the official vendor of BO Pass. I will purchase directly with them.
