In returrn you quote from an unnamed source about the penance in relation to Confession. So? First, it has nothing to do with the purgatory. One suffering in the prugatory is not paying for any sin; he already has his sins repented of, confessed and absolved. Second, when, during our lifetime we go to confession and receive penance, we are not paying for that sin either. Christ alone paid for every sin. A Penance is to strengthen the penitent against future sin. For example, if a penitent went to confession, got the sin absolved and got a penancer assigned, and then did not do penance (for whatever reason), that sin that he confessed remains absolved. Why? Because Christ paid for it. It helps to know something about that which you attempt to opine.
You then continue quoting: they yielded to some temptations, fell into some small sins
Yes. But again, Christ paid for these small sins as well. The Church Suffering is in purgatory because they need to be pure, not to pay for any sin, big or small. This is, by the way, what your unidentified source is saying, -- you did not have to make this post and pretend to argue with me at all. You simply needed to read from that source as it seems to know what sin, penance and purgatory are quite well.
Then what is purgatory purifying people FROM?
THE WORKS OF SATISFACTION It [the council] teaches furthermore that the liberality of the divine munificence is so great that we are able through Jesus Christ to make satisfaction to God the Father not only by punishments voluntarily undertaken by ourselves to atone for sins, or by those imposed by the judgment of the priest according to the measure of our offense, but also, and this is the greatest proof of love, by the temporal afflictions imposed by God and borne patiently by us.