I've been working with a person in the UK and recently fell into some issues. There's breach of contract being thrown around. I'm just wondering which jurisdiction it would fall under: UK or international? There's no professional contract, just emails. There weren't any clear terms and estimates weren't always given upfront. Now, I'm being charged for more money for editing and money already paid. Just like to know what is legal. thank you.
"There's no ... contract" - wrong! The emails are the contract, see What is a contract and what is required for them to be valid?
If you didn't agree on which laws will apply then that is a matter for the court to determine. In general, they will tend to look at where the bulk of the work was done - since you are being charged I assume the work was done in the UK so probably UK law applies, noting that the UK is actually 3 different jurisdictions (England & Wales, Scotland and Northern Ireland).
That said, many jurisdictions have non-excludable laws around contracts, particularly consumer contracts that apply irrespective of the substantial law applying to the contract. It is therefore possible that you apply English contract law subject to, for example, Australian Consumer Law. Usually any consumer protection law in the vendor's jurisdiction will also apply.
General contract law dictates that where a price was not agreed a reasonable price must be paid. If its reasonable that the editing should have been included in the original price charged then you don't have to pay more but if it isn't then you have to pay a reasonable amount for it. There is generally no requirement for estimates or any other method of determining the price - you just have to do what's reasonable.
However, consumer protection law generally imposes more obligations on a business than general contract law.
It is likely that your contract is ambiguous - courts will endeavor to fill in any ambiguities to make the contract work. techniques include read in implied terms to give "business efficiency", from custom or business usage (e.g. if particular industries typically deal with particular issues in particular ways), from previous dealings (i.e. what the parties have done in the past), from statutes, whatever works to resolve uncertain, meaningless or ambiguous terms, from the express words used or from the nature of the contract or from the common intention of the parties (i.e. the court might ask you what you meant).
"Breach of contract" is a very broad term - it simply means that one of the parties hasn't done what they were required to do and allows the other party to sue for damages.