At B- and up, I can pretty much compete for anyone if I'm willing to go all the way in on promises and visits, assuming I have a not-awful preference match, and can devote a reasonable number of APs. Obviously, it's better if those kids are local, where going all-in doesn't suck up half my budget. At C+ or lower, I think twice about going all in for anyone I think a big fish may want, because at 2 full prestige levels, you start getting knocked out of signing range when your opponent matches your effort/promises.
Scenario 1 - if preferences are great, and the recruit is worth it, maybe. But I'll start with promises. Sometimes those are enough to keep others moving on. I don't do visits for kids that far away until I have to.
Scenario 2 - 800 miles is a little out of my typical all-in range. I usually only scout out to about 400 miles in the east, 750 in the west.
Scenario 3 - the only "bad" preferences in this scenario I'm even looking at are style and conference strength, and even for those, I'm not too concerned, if it's a guy I'm willing to offer promises to. If the guy wants a rebuild, I'm not worried about bigger programs having a better match. And if he wants to go far away, I'll still have a pretty clear advantage because going all-in is considerably cheaper for me than anyone who would get this advantage. For offense and defense, the worst I can be is neutral. I'm at the point where my longevity and conference strengths are at worst neutral. And I personally don't think style matters all that much. Even if it does, one bad match can be overcome with AP effort.
The key in all scenarios is whether this is a guy I'm willing to offer promises to. If I am, I offer them as soon as possible, and always before extending any visits.