I'll try this again...
1. What are "regional presbyteries"?
I suspect this is a newspaper's attempt to be helpful to people who don't know the Presbyterian system. Changes to the constitution have to be ratified by the presbyteries. There's only one kind.
2. I (currently) attend a PC(USA) church in a state that does not yet allow same-sex marriages. Given the votes in the General Assembly, how does my particular church define marriage today?
Thanks.
What is in effect today is the authoritative interpretation. It allows gay marriage in states where it is allowed in civil law. Thus there is no change for your state. I'm not sure whether this answers your question. If you are asking about the definition of marriage, independently of whether you can conduct it, the Directory for Worship currently defines marriage as a civil contract that is also a Christian covenant. So there's no separate definition of marriage, independent of the state's. That's why it is plausible to interpret the Directory as authorizing gay marriage now.
(Remember that an AI can't change the constitution. The argument would be that the Directory currently ties marriage to the state's definition. It was written in terms of a man and a woman because at the time it was written all states defined marriage that way. Now that some states allow gay marriage, if we accept the state's definition of marriage then we logically would allow gay marriage.)
If a gay couple married in another state moves to your state, I think a straightforward reading of the text would be that we would regard them as married. The civil contract that according to the Directory defines marriage would still be in effect, even if your state doesn't recognize it as marriage.
I think it's fairly weird to define marriage primarily as a civil contract. The wording in the proposed amendment seems to change that, but it still ties eligibility for marriage to civil law.
But if you're interested in the definition, independently of the practical question of when it can be done, that's more complex after the amendment. The text ties the availability of a marriage service to civil eligibility: "If they meet the requirements of the civil jurisdiction in which they intend to marry, a couple may request that a service of Christian marriage be conducted.." But there is now a separate definition of marriage: "Marriage is a gift God has given to all humankind for the well-being of the entire human family. Marriage involves a unique commitment between two people to love and support each other for the rest of their lives. The sacrificial love that unites the couple sustains them as faithful and responsible members of the church and the wider community. In civil law, marriage is a contract ..."
Thus you can argue that we define marriage independently of gender, but tie authorization to perform it to eligibility under state law. This wouldn't typically matter. But if a gay couple married in another state moved to your state, the implication is that we would regard them as married, whatever your state law might say. While I argue above that that's true even now, I think it's clearer after the amendment.
Of course it's pretty clear that the Federal courts are in the process of extending gay marriage to all states, so I believe it's just a matter of time.
Both the AI and the proposed amendment are clear in allowing the pastor to refuse requests to marry, and in allowing the Session to refuse the use of church property.
Note that it is already possible in your state for a Presbyterian pastor to conduct worship services not mandated in the constitution, such as celebrations of a gay union, whether it is a civil marriage or not. This has been possible throughout the history of the controversy over homosexuality. Thus it was already possible to have a service to bless a gay marriage that has been performed as a separate civil marriage. It just wasn't allowed to perform an actual gay marriage.