Is there a difference, really, between persuasion and proof?
Yes. There are many proofs of the Pythagorean Theorem, though someone may not be persuaded by them (especially if they do not take the time to understand any of them). And people are often persuaded by fallacious reasoning, which obviously is not a proof of what the person is persuaded of.
Is certainty anything more than a feeling in relation to sentences?
- the state of being certain.
- something certain; an assured fact.
Certainty | Define Certainty at Dictionary.com
- free from doubt or reservation; confident; sure: I am certain he will come.
- destined; sure to happen (usually fol. by an infinitive): He is certain to be there.
- inevitable; bound to come: They realized then that war was certain.
- established as true or sure; unquestionable; indisputable: It is certain that he tried.
- fixed; agreed upon; settled: on a certain day; for a certain amount.
- definite or particular, but not named or specified: A certain person phoned. He had a certain charm.
- that may be depended on; trustworthy; unfailing; reliable: His aim was certain.
- some though not much: a certain reluctance.
- Obsolete. steadfast.
Certain | Define Certain at Dictionary.com
With definition 1, for example, it is a psychological matter, but with definition 4, it is not merely a psychological matter. So the answer to your question depends upon which definition of the term you are using.
Is rationality just the polite name for rationalization?
No. They are quite distinct, as even a reading of the definitions in an ordinary dictionary will indicate, and is further supported by a study of logic.
Is "rationalization" what we call the rationality of those we do not agree with?
No doubt, some people do that, but they are wrong to do that.
Is all claim to universal truth ground on a leap of faith?
These are questions, not statements.
You will need to explain how you are using those expressions in order to answer your question, except to say that a leap of faith is no real grounding at all; it is a confession that one has no grounding.
With some uses of "universal truth", there is no leap of faith. If I say, your hand will burn if you stick it into a flame and hold it there, and that is universally true, this is something that has a foundation and support, not something that it requires a leap of faith to believe. You may test this for yourself if you wish, though I recommend that you just take my word for it in this instance. But if you are dogmatic in imagining that there is no real truth, then I strongly recommend you stick your hand into a flame until you come to your senses.