1) lumbar puncture goes within the intra=thecal space to collect CSF... It is done at the lumbar level mainly to avoid hitting the spinal cord (the cord itself usually terminates at L1 to L3 depending on patient size/age/anatomy), the only nervous structure left within the dural sac are the nerve cords running down, and these often roll away from the needle.
2) spinal: same idea as a lumbar puncture, except instead of collecting fluid - you are administering fluid into the CSF - and the site of entry can be anywhere along the spinal cord (cervical to sacral - except most people don't do cervical anymore
3) epidural: the needle never enters the dural sac (or at least it isn't supposed to), it is done with a loss of resistance technique (read about that) and the catheter is threaded into the epidural space. as far as the purported story you gave of the epidural needle, it doesn't make much sense... if the cord had been hit by the needle the patient would have experienced other neurologic events (paresthesias, pain, etc). The most likely reason the patient went into respiratory arrest is more likely due to the level of anesthesia/analgesia obtained via the catheter. For example, if an epidural drug is hypobaric/overdosed and ascends along the cord to cervical then patients can stop breathing... very different from "entering the central canal"... trust me, if the central canal were entered then true neurologic damage would have occured at least causing horrible extremity pains, hyperreflexia and most likely ending in catastrophic para/quadriplegia (depending on height of lesion)...
lumbar puncture is way easier than non-lumbar spinals (ie: thoracic/sacral) and is way easier than epidurals...
for GLOBALRN, the argument that some use for not using local anesthesia is that the needle used for most spinals is small to begin with (22 to 27 gauge) - but there are numerous layers to penetrate, and it isn't uncommon to strike bone while searching for the dural sac.... this is painful, and i think as a "patient advocate" patients prefer local anesthesia. you can use pretty much anything (mainly as long as it is preservative free in case of accidental intra-thecal injection) - i like 1% lidocaine (also known as xylocaine), and i often use my topical anesthetic needle as the finder-syringe: meaning i create a wheal at the skin surface then enter in the intended direction and attempt to anesthetize the planned tract of the LP/spinal/epidural.