What is the way God has prepared for man to be saved?
Baptism
Dying in state of grace (no mortal sin)
Belief in divinely revealed doctrine. Available in the Bible or as summarized in the Catholic Catechism
http://www.usccb.org/beliefs-and-teachings/what-we-believe/catechism/catechism-of-the-catholic-church/index.cfm
Being a practicing member of the Body of Christ in the Church founded by Jesus.
Prayer and the Sacraments
Paul assures us that God wills all men to be saved (1 Tim. 2:4). He must then have provided the means for that will to be accomplished, which means salvation must be at least possible for everyone.
In His wisdom, Jesus did not want to leave us
orphans and unaware of our need for salvation, therefore
He established the priesthood as a perpetual reminder of the gift of salvation He won for us on the Cross.
Secondly, is there are way for a non-Catholic sinner to know that he or she has been permanently reconciled to God that does not entail joining only the Roman Catholic church and giving alms to it?
One will know for sure upon death.
Obviously live a sin free life with the help of the Sacraments.
God is the judge and will see what is in one’s heart and will have mercy but be fair.
I personally feel that a baptized Catholic that leaves the Catholic church will have trouble.
Many are invited, but few are chosen.
Here is an answer to your question:
http://www.catholic.com/quickquestions/whats-the-correct-understanding-of-no-salvation-outside-the-church
However, for those who knowingly and deliberately (that is, not out of innocent ignorance) commit the sins of heresy (rejecting divinely revealed doctrine) or schism (separating from the Catholic Church and/or joining a schismatic church), no salvation would be possible until they repented and returned to live in Catholic unity.
The Catholic church is entirely a voluntary organization and their is no legal requirement to contribute to the Church, yes a moral one to support the local parish. I am not aware of anyone being prevented from participating in the Catholic Church because of any requirement of giving alms.
Sincere questions for you or any Catholic reading this thread.
I do hope that this is a sincere question and I have tried to answer as honestly as I can
There were several articles reference in posts 7, 9, 10 and 23 that may also help.
http://www.catholic.com/tracts/are-catholics-born-again
http://www.catholic.com/magazine/articles/salvation-for-non-christians-explained-sola-scriptura