First of all, setting up one's mind against the known mind of the Church simply means to oppose a doctrine divinely revealed and as the Church defines and understands that doctrine. Hence, it does NOT follow from Fr. Bouscaren-Ellis' definition that the Church is the one that must establish pertinacity before a judgment of pertinacity can be reached by the simple layman, for example.
Secondly, St. Robert Bellarmine in your quote is distinguishing between those who are only suspect of heresy, which would require canonical warnings, vs. those whose pertinacity in heresy is plainly evident (i.e., cut off from the Body of Christ themselves). The consequence of the latter falls under Divine Law. That's why I wrote earlier that heresy per se separates the public manifest formal heretic from the Church. The consequence of the former falls under Church Law (i.e., establishing the crime).
Nope.
One whose pertinacity is clearly established is not under mere suspicion, and for the Church to have established it, means they have already declared it.
How this is all so is contained in the SS article I posted subsequently.