Baptism alone does not save, in the same way that Faith alone does not save.
False. A valid sacramental baptism saves.
If you understand the true teaching on Justification, you will understand that even Baptism of water will not itself save a man unless he also have Faith and cooperate with Gods grace.
Here's your problem. You are incorrectly using these terms, and causing confusion.
1. The common understanding of "baptism of water" implies that it is valid, which further implies the person was properly disposed, which further implies they had natural faith.
2. If one has been properly baptized, then they have received Supernatural Faith, which saves.
3. One cannot have Supernatural/salvific Faith before/without the sacrament of baptism.
4. If you are arguing that one can have Faith before/outside/without the sacrament, this is heresy.
5. If you are using the phrase "baptism of water" to simply mean the pouring of water upon a person who doesn't want to be baptized, then your phrase is wrong and confusing.
Having Faith.. I.E. being in the bosom of the Church.
There is natural faith and supernatural faith. Supernatural Faith ONLY comes from the sacrament of baptism. Ergo, only those who are baptized can be in the bosom of the Church.
"Having Faith" refers to natural faith, which, as Scripture says, "comes from hearing". This is also akin to "having the will/desire" to be a member of the Church. But no one can WILL to do anything supernatural; this is heresy. All things supernatural are a gift from God, which we can ONLY get from the Church, through the sacraments.
If by "having Faith" you mean being sacramentally baptized, then I agree. But again, your language is imprecise.
A heretic could “shed blood” for the Church, but would not be saved as he is outside the church.
An unrepentent heretic, I agree. Typically, a heretic refers to a former member of the Church, which means they were already baptized, so all that they need to do to be saved is repent and confess. I doubt an unrepentent heretic would die for the Church. Seems contradictory. But if they did, yes, they would not be saved.