>>19
Very well. Let's first simplify your objection; it amounts to "How can curved space make two objects physically move in relation to another", right? If the sun can accelerate an object that initially was at a relative stand-still towards it, then it follows that it can accelerate each individual atom of a comet, and that it can do so slightly differently, leading to the destructive forces you mention, etc.
So how does gravity accelerate objects? Let's take two appropriately-sized objects, like two planets, and place them next to each other. They'll start moving towards one another. How, you say? They're not moving, so why would the shape of the space matter? Wrong! They're actually moving as fast as they can, timewards (the direction of which is relative, of course, but let's use the starting speed of our planets as a FOR.) So our planets, both continuing in a straight line at constant speed, shift course towards another (and thus go slightly slower timewards, but hardly noticable). Thus, motion.
So back to the Roche limit. The comet is moving through space, but very slowly. It's mostly moving timewards. It is held together by its own gravity, which means space curves around it so its particles, traveling in a straight line, tend to move closer to another (other forces stop the particles, keeping them in place (and making their path non-straight?))
Enter the sun. The sun also curves space. At a point, the space-time the comet inhabits will begin to curve the other way, dispersing rather than collecting the travel lines of the comet's particles. When this tendency becomes stronger than other forces holding the comet together, the particles separate, disintegrating your comet.
tl;dr 1: It is not the curvature of the space-time itself that give the effects you describe, but the effect of previously parallel direction lines passing through and becoming non-parallel.
tl;dr 2: Relativistic gravity normally is very close to Newtonian gravity. Thus of course these phenomena will happen very similarly to in Newtonian theory. If you accept that both theories predict that apples will fall to the ground etc., tidal forces follow trivially.