Does excommunication of a clergyman automatically follow a removal of his Holy Orders, temporary or permanent? If so, does the lift of said excommunication automatically reinstate him into the clergy?
Clerics can be subjected to various censures, such as withdrawal of faculties, suspension, and dismissal from the clerical state. The first two are usually temporary penalties and dismissal is, as far as I know, considered permanent and rarely reversed. Excommunication is a separate penalty, which may or may not be associated with the ones I have mentioned. It depends on whether the priest commits an act that has an excommunication attached in Canon Law. So no, it does not automatically follow; however, the reverse is true: if a cleric is excommunicated, he may not celebrate the sacraments or hold any ministerial part in a liturgy or exercise any ecclesiastical office: his faculties are effectively suspended, plus more.
Excommunication is also expected to be temporary; it is a medicinal penalty, not punitive, it is imposed in the hope that the person will return to unity with the Church.
Also, can a Bishop who has been excommunicated validly ordain persons to the priesthood, even being illicit? If not, then if said excommunication is lifted of said Bishop, the persons not validly ordained must be ordained again properly, no?
A cleric who is excommunicated still validly confers sacraments, but illicitly. Clerics ordained by such a bishop may be automatically excommunicated with him, depending on the circumstances, but a valid ordination will not and cannot be repeated, since it causes an ontological change in the soul of the subject.
The sacrament of Penance requires jurisdiction in addition to faculties in order to be valid. A priest without jurisdiction cannot validly absolve penitents, this jurisdiction is normally granted by the ordinary. I do not know the circumstances under which it can be lost.
