What I try to do is apply some rational standards to the text. I assume the text stands as written, that it was meant to be understood by its original readers/recipients, that it was meant to be used for judgments, that people are different culturally but not inherently different by nature.
As for what I said about the father: I'm synthesizing a great deal of biblical data on households and responsibility, etc., as well as input from the more widespread ANE culture. If you are a student of Scripture, you need to be aware of the cultural milieu in which Israel operated for over 1500 years. When I say the father has some duty to prevent this kind of harm to his daughter, I am simply stating a general fact of human responsibility, taking into account the specifics of the Hebrew culture as the Bible describes it, in the larger context of the ANE.
If an ancient Israelite man lost his daughter's honor this way, that'd be a major shame on his face, far worse than today when many modern fathers blithely send their daughters off to college believing them to already be "experienced" or bound to get "experience." Some of this protectiveness is still has strong cultural currents in the M.E., and other parts of the world.
As for the assailants story: again, assuming the ancient court-of judgment scene where cases like this are actually tried, you have to set it up in your mind. You have (at least) two parties to judgment. Here's the girl, there's the guy, there's the girls father. Now, what are the possible attitudes present? What are the possible pleas? Who stands with whom? What assumptions are safest for the judges to begin with?
The guy may be facing the death-penalty for kidnapping, depending on the witnesses, the evidence, what the girl says. The minimal facts of the case are that the man is accused of having lain with the girl inappropriately. His best defense, if the intercourse is not in dispute, is that the occasion was consensual. But the witnesses may say that they saw him take the girl by the arm and propel her away. Was it force? Was it contrary force? Was it simply hurry?
The set-up for the case lets the situation look as bad as possible for the guy, but it still allows for an outcome that is short of the death-penalty appropriate for a proven kidnap and/or rape. Why? because beside the guy, the father or the girl may prefer a different outcome. Lacking the requisite evidence or witnesses, proof of the worst-case scenario may be lacking.
The case presented doesn't include this: that the evidence and witnesses are all against the guy. It simply tells us that a man seized an "available" woman, and took her to bed. Can't you imagine a situation where this takes place in the modern world, say at a nightclub, or a campus drinking-party? It ends up being his-word, against hers, maybe. Perhaps she can hardly deny her culpability. It could be that the best course, for all concerned, is that the two numskulls get married--no possibility for getting out of it by divorce later, either. Or maybe the father just demands satisfaction (in $$ terms), no wife in the bargain, and takes his girl home with him. Maybe that's better than the man's blood to him? Maybe the guy gets sold into slavery to pay this debt?
The situations are presented for different reasons (in Moses' contexts), and they each present a slightly different situation: one where the situation is no doubt consensual, but the man is deemed the instigator (Ex.22), and one where the consent is more ambiguous, at least to start with (Dt.22).
I think an analysis of the situation in 2Sam.13 (read for yourself) might lend itself to an understanding (though not likely a good application) of the second case. This is a "worst-case" scenario, in which undoubtedly a rape occurred (hideous to think of it), and it was just as surely against the incest-laws, Lev.18:11. Tamar under threat of attack begs Amnon to request her as a wife from David rather than forcing her, and afterward she cries out against--as she calls it--the worse injustice of casting her out. I don't know whether she hoped the king would somehow compel an indissoluble marriage, per the Dt.22 law, and so salvage some dignity from this tragedy, by an after-the-fact solution.
Despite the lack of true parallels, that event does show us a woman, in the Heb./ANE situation, who is a victim, who nevertheless apparently prefers a marriage to her captor, rather than a more ambiguous settlement, one very likely to end in spinsterhood.
Direct answers to other questions:
1) I mentioned "signs of assault" because I find it hard to imagine if someone were (for example) found tied and gagged, whether in a city or field, that the assumption would be that the girl (betrothed or otherwise) was on a lark. The situation, before the court, presumes there is ambiguity, it presumes that there's some question or contention that this was/wasn't a kidnap. I'm not saying there aren't guys who beat up their wives and girlfriends and often the women don't immediately press charges at the first chance; but if you find the girl and she's got two black eyes, fat lips, cuts and blood and other injuries, that's points for her in most jury's eyes if she says she was never willingly with the guy. "Try talking your way out of that one, pal."
2) It isn't used the way you have listed it as "most of the time" when we find it in NT Scripture. The word (I believe it is participle of biazo) generally refers to all sort of force and aggression (see only Mt.11:12; Lk.16:16), but you need a context every time. The LXX is simply making a very literal rendering of the Heb. original, which is to lay hold or seize. I glanced at the Liddell-Scott Gk Lexicon, and I don't even find "rape" listed as a gloss. But, its possible that in some context (and this one is a candidate), forcible intercourse is the understandable result. But I fail to see how the LXX is going to tell us better than English what the Heb. intends, instead of preference to the Heb.
The woman is forcibly taken off, but strictly speaking, we don't know whether she's unwilling, compliant, consensual, or anything else. The word "taphas" (seize) isn't so connected to the "lies (with)" as to make it a compound idea (construct-chain). The verbs are distinct but consecutive, separated by the vav. But one simply can't state that the force and the intercourse are coterminous. And I've given already some scenarios that demonstrate that rape is not a necessary conclusion from the language.
Another that comes to mind is the notion that the "seizing" could very well be in connection with her present guardian (father). That is, she is "seized" from his protection (which maybe she resented). How much force, and what kind, are the sorts of questions that the judges must determine.
I'm not saying that taking her from the father IS the probable sense. I'm saying that to say that this verse is definitely talking about a rape-scenario IS reading a specific definite sense into words that are susceptible of alternate, legitimate understanding. The courtroom scenario is the place where this case is interpreted and judged. And in the case judgment preserved for us, the man is given a monetary penalty, he keeps the woman as wife (without possibility of divorce), the woman is presumably willing to stay in that situation, and the father of the girl is mollified. Seems clear to me, they decided the case wasn't strictly kidnapping, however much force was involved, and who was victimized, by what means.