1) A small cut can be easily healed by stormlight. A small cut in the heart is still a small cut. Plus, one does not beed to breath when holding stormlight, so maybe the loss of blood pressure doens't make you go uncouncious while holding it.
She didn't drown in shadesmar because, as she demonstrated twice before, she is much more adept at manipulating it than Shallan. And she was at the sea, wich is solid in shadesmar anyway, so it doens't even matter.
2)She wasn't murdered. A wound in the heart is not necessarily an instantaneous death, especialy if you have supernatural healing.
3) See the two previous points. You are overestimating the effects of a heart wound in a surgebinder.