No, sorry. I try to be deferential when talking about this stuff, but this is pretty cut and dry, and I’m afraid you’re just wrong here. This is Greek–not theology. πίστις is the word we’re talking about. It shares the common root with πείθω–“to persuade” (i.e., that evidence is compelling or trustworthy). πίστις is the same word you would use in describing the veracity of a tribunal’s judgment (for example, “I have πίστις that the jurors in NY got the verdict right/wrong”). The Greeks used the word to personify honesty, trust, and persuasiveness prior to the existence of Christianity (although someone who knows Attic or is better versed in Greek mythology feel free to correct me). The word is inherently tied up with persuasion, confidence, and trust since long before the New Testament. The original audience of the New Testament would have understood the meaning of the word without depending on any prior relation to religion.
Is trust always a better translation? Of course not–and that’s why, you’ll notice, I didn’t say that (and if it were, one would hope that many of the very well educated translators of Bibles would have used it). But I think you can agree that the concept is also difficult for English to handle (since trust in a person, trust in a deity, and trust in a statement are similar but not quite the same thing, and the same goes for belief in a proposition, belief in a person, and belief in an ideal or value, to say nothing of analogous concepts like loyalty and integrity).
The point is that πίστις–faith–absolutely does not mean belief without evidence, and Christianity since its inception has never taught that. English also doesn’t use the word “faith” to imply the absence of evidence, and we don’t need to appeal to another language to understand that. It’s why the phrase “blind faith” exists (and the phrase is generally pejorative in religious circles as well as secular ones).
Now, if you think the evidence that convinces Christians to conclude that Jesus’ followers saw Him after His death is inadequate, that’s perfectly valid and a reasonable criticism of Christianity–and if you want to talk about that, that would be apologetics.
In any event, if you’re going to call something bullshit, you better have a lot of faith in the conclusion you’re drawing. ;)
It’s a broad generalization, but it’s not really a matter of opinion. We can scan people’s mouths and faces when they talk (and have in order to demonstrate this stuff). I think the last example probably only applies that way in particular circumstances though, since English speakers automatically group, contract, and arrange certain phonemes in certain orders (e.g., I’m not, I ain’t, but never I amn’t–and in real speech “I ain’t” is almost always one syllable). In this example, more frequently my country ass contracts the first syllable of “gonna” away instead of the second, so “I’m 'na head to the store; y’all need anything?”
The hot potato example just stands for the premise that in real speech the t at the end of hot and the p at the beginning of potato slur together, and if you deliberately enunciate both consonants, you sound like you’re reading to a transcriber. Compare the way a normal person says “let’s go” to the way you sound if you force separate the words: you sound like you’re doing a Mario impression.