Like I said above, Picard's laughter (if he even laughed) was probably a physiological or nervous reaction to what was going on. Stabbing someone in the heart won't prevent them from laughing, physiologically speaking, as it has no connection to the lungs, vocal chords, diaphragm, or any other physical part of his anatomy except for maybe the chest cavity, but he would ignore that in the first few seconds. He's likely going into shock, as he expressed no pain from the sensation. But, of course, his memories of the event were almost certainly glorified, as he describes it in Samaritan Snare differently to what we see in Tapestry. The pain from the stabbing would have included the sudden jolt of a severe heart attack on top of being skewered by that serrated knife.
Keeping him alive would've been nominally easy. Sedate him and toss him into a stasis unit, then await a medical professional. He was probably hooked up to machinery, and made the personal decision to have an artificial heart (and thus, live longer with the risk of a potential catastrophic failure), versus a corrected or cloned biological heart (probably a shorter lifespan but less risk of catastrophe). Given that Picard was a marathon runner, previously, he probably opted for the artificial heart to keep a similar lifestyle, whereas anything biological would've taken too much adjustment and medical care. And he was certainly pushing into getting back into service quickly.
