I would divide questiona I am asked in two groups:
1. Questions Protestants SHOULD ask, but all to often they don't;
2. Questions they actually ask;
The Orthodox, by the way, tend to know the Catholic answer and most times the Orthodox answer is the same answer. So, I narrow your question to Protestantism as the source of the question.
In the first category are the fundamental questions of faith:
A. Relationship between the Catholic clergy, the Holy Tradition and the Holy Scripture.
B. Relationship between faith, works of love, and liturgical works.
C. Meaning of the Sacraments of the Church.
D. What is Communion of Saints?
E. What are particular and universal judgement?
Anyone who would satisfy himself with the answers to the above would not need to ask questions that he indeed asks. They are:
Instead of the fundamental question
A. Relationship between the Catholic clergy, the Holy Tradition and the Holy Scripture.
we get asked:
- where in the Bible is ...
The answer, invariably, is that the Bible is a part of the deposit of faith given us by Christ. Our practices and beleifs are not necessarily inventoried in the Bible. However, they do not contradict the Bible.
- Why do I need to go to a priest to confess a sin or take communion?
The answer is that Christ sent the bishops and priests like Himself ("like my Father sent me so I send you"; "feed my sheep"; "whose sins you forgive they are forgiven them"). He did not send the laity like Himself.
- Why don't you have woman priests or married priests in the Latin Rite?
The answer is that priests imitate Christ Who is male and married to His Church.
- Why don't you read the Bible?
The answer is, we do and we should do so more, but we do not interpret the Bible ourselves as we read it. We study how the Church interpreted the Bible historically through the ages.
- Why do you pray to icons and statues?
The answer is that we pray to God with the help of the saint who is depicted in the holy image. The Church taught us the proper meaning of such prayer, as well as taught us not to fall in idolatry.
Instead of the fundamental topic
B. Relationship between faith, works of love, and liturgical works.
we are asked
- why do you think one can earn his way to heaven? Doesn't it makes Christ's work incomplete?
The answer is that Christ alone makes our works of love and liturgical works possible, and He asked us many times int he scripture to do these works in order to increase our faith. We are saved by grace with faith working through love, just like the Scripture teaches.
- why are you so hung up on the ritualistic; didn't Christ condemn rituals?
The answer is, Christ condemned empty rituals and we condemn them too. The sacraments of Baptism and the Eucharist are explained and mandated in the Scripture in great detail; all other sacraments are at least implied. The Church develops the proper reverent form for these on authority of Christ our King.
Instead of the fundamental topic
C. Meaning of the Sacraments of the Church.
we are asked why we bow here, kneel there, cross ourselves, baptize children, don't allow remarriage after divorce, do five Hail Marys for penance, insist on fermented wine and wheat bread for communion, etc. All this interest in form and detail is the result of a lack of understanding of the meaning of each respective sacrament, and the proper role of the hierarchy of the Church in defining the form.
Instead of asking
D. What is Communion of Saints?
we are asked
- why do we pray to Mary and saints and dead souls?
If the person understood the communion of saints as souls living the everlasting life with Christ in Heaven, as was promised them and us, we would not be surprised that we consider ourselves constantly in their company and that they pray to Christ, our sole mediator before God the Father, for us.
- why do we have monks and nuns?
Because we consider prayer the most important part of our
lives, but we in the world do not always have the time.
E. What are particular and universal judgement?
If one understood that one's soul is judged immediately upon his death, but the world as we know it comes to an end with the second coming of Christ for us all, one would not wonder why
- we believe in Purgatory?
- pray for the dead?
- think that suffering and virtuous acts in this life helps our own soul and souls of others?
Indeed, the concept that the soul that is saved by the mercy of Christ upon death often needs purification before it can join Him in Heaven follows logically from the fact that we die with impurities but only pure souls can be with Christ till the end of the world and beyond. Once this framework is in place, the scriptural references to purification after justification such as in 1 Cor 3 begin to make sense.
Great summary!