Once again each diocese is different.
In some ways, yes.
Two different things can be envisioned here. One is the transfer of a deacon within a diocese, and the second is his temporary or even permanent movement from one diocese to another. The latter involves various permissions and ultimately the consent of the bishops from both dioceses. If permanent, it is called excardination (leaving one diocese) and incardination (entering the other). Canons 266-271 describe and regulate the process for the Latin Church.
As to transfer within a diocese, the assignment of a deacon to ministry, as it is with any cleric, pertains to the diocesan bishop, or in the case of a deacon who is a vowed religious (since religious communities of men may also have permanent deacons who are, of course, celibate), his superior who is competent to do so.
Assignment to a ministry is not the same as parish membership, strictly speaking.
Only a priest can be appointed as a parish administrator according to law, since a parish administrator has almost all the rights, duties and powers of a pastor. In practice, non priests have been appointed to do the daily work of a parish administrator, but a priest is also appointed as canonical pastor. (Canon 539: When a parish becomes vacant or when the pastor is prevented from exercising his pastoral office in the parish due to captivity, exile, banishment, incapacity, ill health, or some other cause, the diocesan bishop is to appoint as soon as possible a parochial administrator, that is, a priest who substitutes for the pastor in accord with the norm of can. 540.)
The death of a deacon’s wife does not indicate one way or another that the deacon is suited to the ministerial priesthood. These are separate functions and consequently different vocations. The question must be open to discernment by the deacon, the Church, and the diocesan bishop. Most recently, the praxis has been to discourage widowed deacons from seeking priesthood.
