If a person is said to be a vegetarian, and then one day eats meat,
is that person still considered to be a vegetarian?
No, because the definition of vegetarian is one who abstains from all meat. I suppose one could say that they are "mostly vegetarian" but I have heard some vegetarians take issue with that, that calling oneself "mostly" does not apply either.
If a person is said to be faithful to his or her spouse
and then one day, decides to have an extramarital affair
is that person still considered to be faithful
--even though they are still considered to be married?
No, he or she would no longer be a faithful spouse, by definition. However, he or she could still be married, that is up to the couple to work out and decide.
If a person is said to be a buddhist
and then kills a group of people,
is that person still considered to be a buddhist?
Yes, because a Buddhist is not automatically a Buddha or arahant or necessarily any higher level of attainment. It is good to keep the precepts, but how many Buddhists really keep all 5 precepts all the time? I imagine many Buddhists struggle to keep the alcohol abstention precept all the time, violating it for social encounters. And I am sure many Buddhists sometimes tell some white-lies. I am not condoning or approving the breaking of any precepts, just stating the reality.
When people say, "that killer was a devout buddhist"
what is your response?
It was a mental health issue, not about his religion.