If you wanted to leave out the 'which is', you'd need to add a colon to the sentence. "The printing process has only one primary function: to put the ink on paper."
I don't think there was ever a doubt about "primary" being an adjective or about its meaning. The sentence is not redundant. I thought this would be quite obvious, but I will have to explain things in a simpler way in the future.
Primary doesn't imply uniqueness; so stating "only primary" isn't necessary if you're just talking about primary functions, it is if you want to make it clear that there is only one primary function.
It depends on how much the audience knows about printers actually. I'd say they were all good solutions depending on what the person you're talking to knows. In my case for example, I'm not entirely sure if the printer just has one primary function or if it perhaps has two (maybe collating, as that's a feature I find to be important). It's entirely possible to have a single primary function, sing