Can I tutor for Crib Swap with rebels like Ramosian Lieutenant? If so, does it get cast like normal, or enter the battlefield as some sort of spell-permanent?
Not with Ramosian Lieutenant. That card's Oracle text has changed so that it refers to a "Rebel permanent card", not just a "Rebel card" (C.R. 108.1). In general, an effect that refers to a "Rebel permanent card" as opposed to, say, a "Rebel card", doesn't refer to an instant or sorcery card, even if it has the Rebel creature type as Crib Swap does (C.R. 110.4, especially C.R. 110.4a; C.R. 702.72a, 205.3m).
Moreover, even if Ramosian Lieutenant's Oracle text didn't change and still referred to a "Rebel card", an instant or sorcery card such as Crib Swap would remain in its current zone rather than enter the battlefield (C.R. 304.4, 307.4; see also C.R. 110.4).
Use the Oracle text of a card to determine that card's wording (C.R. 108.1). Compare the first and second abilities of Lin Sivvi, Defiant Hero in its Oracle text, and see also this thread.
Moreover, even if Ramosian Lieutenant's Oracle text didn't change and still referred to a "Rebel card", an instant or sorcery card such as Crib Swap would remain in its current zone rather than enter the battlefield (C.R. 304.4, 307.4; see also C.R. 110.4).
Use the Oracle text of a card to determine that card's wording (C.R. 108.1). Compare the first and second abilities of Lin Sivvi, Defiant Hero in its Oracle text, and see also this thread.