] There was (and is!) a church service for "officially" recognising women back into society like this. It mainly gives thanks for the "safe deliverance" of mother and child and , in JA's England, seems to have been performed at any time that any other services were carried on.
That seems to be the same thing, yes. IIRC (I don't have my notes here) it was usually performed just before high mass on sunday. Women liked it if the ceremony was performed 6 weeks after Christmas, for obvious reasons. ;)
] I don't think there was a statuory time to wait before it was done,though- I think it was when the woman felt herself ready.
There was a law here. 6 weeks up until 1845, then 4 weeks. The tradition declined just befor the turn of the century, and these days nobody has it done.
] The ceremony is called "Churching" and probably goes way, way, back to times when a mother who had given birth was considerd "unclean"... but again, I don't think that particular sentiment really applies to JA's time.
I am quite sure you are right!