I would say that this is good evidence that the Scripture does not rigorously follow our dainty Trinitarian formulas. The Trinitarian formula that is traditionally what we maintain is this: from the Father, through the Son, by the Spirit. But the Scripture does not rigorously maintain any such formula. Sometimes, things are said to be of the Son, without reference to the Father. Galatians 4, The Spirit is said to be of the Son, just as Matthew 10 says that the Spirit is of the Father. This is why it is foolish to place an enormous weight on any one such formula.
It doesn't say that. It doesn't say "from the Father alone" or "from the Father, but not the Son." It simply said "from the Father." If the Spirit is said to be "of the Son" such as it does in Galatians 4 and Romans 8, then the first two views couldn't be rigorously true on a Scriptural basis:
When we receive the Holy Spirit, we do not believe that the Father acted alone but that the Spirit also came through the Son to us.
But this is all false, because the Spirit only comes to the Son after His baptism. Hence any other reference to the Spirit coming to Christ occurs after it proceeded from the Father, which blessed it onto his Son through the sacrament of Baptism.
Ignoring chronology of events is Unscriptural.
Though he was deemed a heretic, he had a lasting influence on the Church for centuries, even to this present day. No different from Tertullian, who also was deemed a heretic, but he remains an influence on us. Even when we use the term 'Trinity' we are showing Tertullian's influence.
We have no idea who influenced who, but none of Origen's works survive so it's impossible to know. We have no idea if it was Tertullian or Tertullian's teacher who taught the trinity. All we know is that early heretics were rejected.
This isn't a religious practice, this was standard Roman crime and punishments that were typical of the era, and predated the Byzantine era, including in surrounding countries. If anything, the introduction of Christianity significantly softened the punishments of criminals in Ancient Rome. Byzantine punishments, while harsh by today's standards, were far more lax compared to Ancient Rome's on many levels. People weren't being fed to lions because they stole something. Merely losing a hand was a big step up for thieves.
I'm talking about the policies specific to the Church - the main way the theocracy was enforced was through the mechanism of citizenship, not by killing anyone who merely did not want to belong to the Church. For the rest of punishments of that time, you have to keep things relative to their context, which was the Ancient Roman world - a savage world.
If you spoke out against the Church in a blasphemous way, sure, you could get punished, because you were also speaking out against the state, but that was exactly the same in the Pagan Roman era that preceded it. Compare apples to apples.
The Papacy used war to enforce their own theological dictates, because they could not strip someone of citizenship. The state model broke down in the middle ages, and calling crusades on heretics was the only card the Papacy had left. In the Byzantine era, people were exiled for heresy generally, it was far more humane by comparison.