this is the time of year when bishops make changes in priest assignments so yes it is the common thing. In most dioceses there is a rule or practice that a pastor serves one term, often 5 or 6 years in one parish and then is moved. It is also common for him to get an “automatic extension” of another term if he requests it and the needs of the diocese allow. However a priest could be moved sooner if the bishop feels his particular gifts are needed elsewhere. These decisions are made by the bishop, usually in consultation with the presbyteral council–an advisory board of priests–to best meet the needs of particular parishes and the entire diocese.
With regard to priests assigned to parishes or other roles not as pastors, again the decision tries to match the gifts of the priest to the needs of the assignment. And no it is not common for an assistant to be moved up to pastor of the same parish. A new priest generally serves a variety of assignments for several years before becoming a pastor, but with the priest shortage, many become pastors rather quickly.
and yes, a priest may ask for a certain assignment and the bishop would honor that if possible and if he deemed it wise. For instance our last pastor asked to be assigned to a poor parish with the most dire pastoral needs, and another has asked for a primarily Spanish-speaking parish to increase his language skills, and another was assigned closer to his ailing parents until they died.
In some dioceses the priests are moved around within their deanery or vicariate (smaller geographic area within the diocese) when possible, but may be moved outside or to the diocesan offices as well.
Catholics should learn not to get attached to the personalities of certain priests and embrace the theology of the priesthood, that every priest, no matter what his personality, background, quirks and foibles, is in the Person of Christ when carrying out his sacred duties.
In this diocese, past practice has been not to move a pastor who is in the middle of a capital campaign (raising money to build a new church) but it is not an iron clad rule.