Should reckoning effects be executed as if done simultaneously?
You get to determine the order of the effects, but they do not happen simultaneously. Thus you should resolve curse effect first and blessings last. 

Do note that if a reckoning effect causes you to gain a card (e.g. a condition) that has its own reckoning effect you do not have to resolve the reckoning effect on the new card until the next reckoning. Basically, once the reckoning phase begins, the list of things that need to be resolved is fixed for that round. 

And, yes, if your investigator is defeated by a reckoning effect you do not continue to resolve reckoning effects on his/her remaining items. Defeats are immediate and you discard all conditions and tokens (except clues) and set the investigator aside along with his possessions. This can also cause you to loose beneficial effects that the investigator was providing to others on his/her space. So, again, the order you resolve the effects does matter, even between investigators where you are supposed to follow the usual turn order (lead first, then clockwise).  

The case in the question you cite is a little less clear. Lost in time and space usually allows an investigator to skip resolving reckoning effects. But you could argue that all the items' reckoning effects are triggered already (just unresolved) and since you take the items with you you have to continue to resolve them all.