It would be the traditional consensus that Catholicity is not lost objectively even by a formal (i.e., not just material but also intended or volitional) act of defection or excommunication. These result in impaired communion with the Church. Hence, with apologies to those who have heard it before, semel Catholicus, semper Catholicus.
The subjective understanding of the individual could certainly be to the contrary. Several responses have focused on that subjective understanding. The topic has been the object of several threads in the past, and the responses have reflected assessing the issue differently, based on that distinction.
A brief piece on this distinction can be found close to this very page, at forums.catholic.com/showthread.php?t=94485&highlight=semel . The opinions from the commentators of the Canon Law Society of America reflecting the objective situation are posted below. They are representative of thinking among canonists.
As noted, simply lapsing in Catholic practice is not a formal act of defection.
I will respond to this canonical condition of such persons in that this presents how the Church understands their objective situation. Now here, the way to proceed is to actually read the canons referenced below. This can be done through the archive library at the Vatican website if one does not have a hard copy of the Code.
So as to the question, “If someone was baptized Catholic, received the sacraments of Communion and Confirmation, then later they renounce their Catholic faith, are they still considered Catholic by the CC?”, the answer is yes, and Catholic baptism or admission by the profession of faith is all that would be needed in view of canon 96. Catholic baptism alone is sufficient. The reception of a person already baptized has the same juridic effect. This also anticipates how we would answer your last scenario later.
From the canonical point of view, not even excommunication renders a Catholic no longer Catholic. This is not an effect of that penalty among those listed in canon 1331. Clearly those, it results in a loss of the full communion which is treated in canon 205, but the fact remains that such an effect is not given in the law.
The formal act of defection mentioned in canon 1117 merely proceeds to except the person from certain ecclesiastical laws though, for example, that of canonical form of marriage (canon 1127), the prohibition against marrying a non Catholic unless there is express permission (canon 1124). Tribunals or other Church authorities often have to evaluate these situations to see if a marriage case requires the ordinary process for nullity or not. However, the law mentions no effect of becoming a non Catholic for the person who defects by a formal act.
So here, if the question is " If they marry outside the church because they say they are no longer
Catholic, are they in a sacramental marriage just as two Protestants would be?," the answer is yes if the other party is baptized. This also answers the question, “Last scenario- if the person had only been baptized Catholic but didn’t receive any other sacraments of the Church, and later became Protestant, would they still really be a Catholic?” Yes, the person would objectively remain Catholic.
Public defection from the Catholic faith or from the communion of the Church removes a person from ecclesiastical office in canon 194.
Now here are those opinions to consider.
“. . . [T]he axiom, ’ once Catholic, always a Catholic,’ reflects the fidelity of God toward an individual - the offer of grace always remains for the individual to accept or reject. From a canonical perspective, the law seeks to preserve clarity in determining who is bound to ecclesiastical laws.” (Robert Kaslyn SJ, JCD, “The Christian Faithful (cc. 204-239)” in New Commentary on the Code of Canon Law commissioned by the Canon Law Society of America. [New York, NY; Mahwah, NJ: Paulist Press, 2000]; p 250; canon 205.)
As James Provost JCD wrote in the 1985 CLSA Commentary (same publisher) on canon 205 (pp 128-129): “Ultimately, the bond with the Church is rooted in something that can never be lost - baptism. . . only the individual can withdraw from full communion. The Church does not expel persons from its midst. Essentially, the heretic, apostate, or schismatic withdraws from those bonds by a personal act. The Church recognizes this in declaring the bonds severed, but they are never totally cut.” He then asks, “Is its then possible for a Catholic to leave the Church? Traditionally, the answer has been no. Baptism irrevocably bonds a person into Christ and the Church, even if that bonding lacks the inner personal commitment of the baptized individual. The radical, constitutional change has been made and is irreversible.”