What would usually go down with a marriage between a Catholic groom & Catechumen/non baptized bride? What would it still have? What would be left out? Is it a valid marriage? How would the procession go? What days is it allowed to be on? What time of the day do they usually go on? Who would conduct the wedding? Is there anything else that is important?
That’s a lot of detailed questions. Have you talked to your pastor about marriage preparation in the Catholic Church?
All couples approaching the church for marriage go through premarital preparation, the specifics of which vary by diocese, and the investigation of freedom to marry which documents that each person is able to marry validly.
And, in the case of a Catholic marrying an unbaptized person, there are additional things that must be discussed with the pastor and through the pastor the Catholic seeks a dispensation from disparity of cult from the bishop to marry the unbaptized person.
Regarding the ceremony, it takes place on any day and time not prohibited by the Church (such as certain feast days, Holy Week, etc). Your pastor will discuss what times he makes available for weddings-- some parishes have many activities and only set aside certain blocks of times while others may be very flexible with the time the couple desires.
When a Catholic marries a non-Catholic, the Marriage Rite is typically done outside of Mass. So it follows the liturgy specified for the Marriage Rite Outside of Mass.
Is there anything else that is important?
Yes, make an appointment to speak to your pastor.