How was Sayaka able to join Madoka in the Law of Cycles after her death? Adding onto this question, right after Madoka recreated the entire universe to accommodate with the Law of Cycles, why was everybody placed back in time right after the event where Sayaka gets killed in battle? Why were they placed specifically there in time? Also, do all magical girls join the Law of Cycles after they die? If they do, then what is the point? Madoka's wish was to erase all witches with her own hands, so anybody else in the Law of Cycles wouldn't have a job to carry out since Madoka would be doing it all herself.
Right after Madoka recreated the entire universe to accommodate with the Law of Cycles, why was everybody placed back in time right after the event where Sayaka gets killed in battle? Why were they placed specifically there in time? 


I don't think it's quite accurate to view everybody as having been placed back where Sayaka gets killed in battle. In this rewritten universe where the Law of Cycles exists, the entirety of history plays out differently, probably diverging whenever the very first magical girl's Soul Gem turns dark. Every scene involving witches or Madoka personally probably plays out differently; it just so happens that we only get to see one particular scene from this new history of the world - the scene where Sayaka dies. Why? Well, it's an important scene, particularly given how that same scene was something of a bloodbath in episode 10's timeline 3. And plus, it helps us understand how the new universe works. 

I find it more likely that everybody was "placed" back at the same instant that Madoka made her wish in the main timeline. (I don't have any strong evidence for this; it just seems to be the most parsimonious option.)




  Also, do all magical girls join the Law of Cycles after they die? 


I'm guessing you haven't seen Rebellion. 


   Rebellion strongly suggests that the answer is yes, based on Sayaka's comments at the beginning of the final segment (shortly after Homura turns witch). Magical girls do indeed become part of the Law of Cycles when they're touched by Madoka when their Soul Gems go dark.





  If they do, then what is the point? Madoka's wish was to erase all witches with her own hands, so anybody else in the Law of Cycles wouldn't have a job to carry out since Madoka would be doing it all herself.


Again, I'm guessing you haven't seen Rebellion, since in Rebellion, we learn that:


   At minimum, Sayaka and Charlotte/Nagisa both sort of exist in the same metaphysical space as Madoka. Sayaka herself notes that the two of them are sort of like "secretaries" to Madoka. They both play a key role in Madoka's scheme to extract Homura from the Incubators' barrier; it seems unlikely that Madoka would have been able to effect her scheme without their (or at least somebody's) assistance.