What is supposed to happen with different types of chemical bonds? If half of a molecule is inside a black hole and half is outside, the half inside is necessarily constrained to the black hole, while a molecule outside does not have such constraint. The chemical bonds should be also necessarily broken at least for a moment, since an atom inside black hole can not exert electromagnetic effects on an atom outside black hole. Wouldn't it create a bias across your whole body with some really weird atomic / chemical consequences?
Nothing happens (locally) at the event horizon, everything works as normal. The analogy that is often used is fish upstream from a waterfall. At some point the current of the stream becomes so strong that the fish can no longer escape from the waterfall, but actually at that point nothing happens from the point of view of the fish, since it is carried by the current, you need a global view to notice that the fish is doomed past that point.
And similar in case of a black hole, you are falling through the event horizon and nothing happens, it is just that calculating what you need to do to escape, you note that it is too late.
To expand a bit on the molecule situation, when one of the atoms is inside the black hole, then parts of its electric field are still outside and influence the other atom. To have the other atom escape to infinity, you would need to break the part of the bond "still outside" and the gravity of the black hole.
> If half of a molecule is inside a black hole and half is outside,
You know how the universe is expanding, such that the milky way is moving away from (sufficiently) distant galaxies faster than the speed of light? But chemistry still works fine here? When you fall into a black hole, you accelerate until you're moving away from the rest of the universe faster than light, but all your atoms are still (relatively, assuming the black hole is large enough to have negligible tidal forces) stationary relative to each other. The event horizon is just the point where your speed relative to the effectively-distant[0] outside universe exceeds the speed of light. Any signal you emit can't be moving facter than c relative to you, so it will always be moving away from the outside universe (v<-c implies v+v'<0).
0: "Nothing can move facter than c" refers to relative motion of objects near each other, which is why the Hubble expansion of the universe doesn't contradict that either.
In General Relativity, locally all reference frames are flat. This does not change at the event horizon, chemistry continues to work normally. It is just that in the time it takes for half the molecule to affect the other half, the other half will have slipped across the event horizon.
There is a classic analogy of light traveling through space-time being like ants crawling on a balloon. A black hole is a spot where the balloon is being sucked in. Faster and faster as you get closer. The event horizon is where the speed at which the balloon moves matches the speed of the ant. There is nothing special from the ant's immediate perception about this line, but if the ant crosses, it is doomed.
