So....your post has been up for two days, 60 some views, and no answers. My guess (and you hinted at it), it may just not be possible to achieve all of those conditions at one and the same time. So which are you willing or able to compromise?
Public access via a website or link
This one is easy by itself. OneDrive or GoogleDrive could be used, the former with Excel, access being granted to individual users; GoogleDrive can be used with either Google Sheets or Excel, though it can be dicey at times.
This strikes me as one of the hardest of your criteria to meet. I'll defer to others on whether it's even possible to grant access without implicitly the ability to download. By "implicitly" I'd include the ability to copy and paste, so that even if I were precluded, a big IF to begin with, but even if, so long as I can see it, it's often harder to preclude copying and therefore pasting. As I said, I'll defer to security experts.
No saving results in the sheet, each user needs a unfilled version to use
Be able to print a copy of values/results in a PDF
Able to add values into specific cells to use the calculator formulae we have created
No modifying on the cells/formulae
All of those above can be achieved by saving the file with Protection of cells that can't be altered, and saving it as "Read Only." But this is a set of criteria that seem to me to fly in the face of the "not downloadable" since, especially, you're saying that each user needs to have "an unfilled version to use."
So maybe you need to refine your criteria and try again......but I invite those with more experience in the field. Is this some academic research? Or is it (let's see if we can start a conspiracy theory) some sort of CIA or FBI clandestine work?