Which currency should my foreign branch keep its accounts in?
The one it actually operates in, which is a question of fact rather than of preference. Look at where the branch earns its revenue, what currency its costs and staff are paid in, how it is funded, and what currency its cash sits in. Those point to the functional currency. Keeping the books in the parent's currency for convenience is common and not fatal, but it creates translation work later, because the foreign return will want results measured in the currency the branch really transacts in. Deciding the question early and writing down the reasons is far cheaper than reconstructing it during an enquiry.
Is functional currency the same as the currency I invoice in?
Not necessarily. Invoicing currency is one indicator among several, and it is often chosen to suit customers rather than to reflect where the business operates. An entity can invoice in one currency, pay its staff and suppliers in another, and be funded in a third. The functional currency is the one the operations are genuinely conducted in once all of that is weighed together. Where the indicators pull in different directions the answer is a judgement, and it has to be recorded with its reasoning, because it determines how every figure on the return was measured and will be the first thing asked about if those figures are questioned.
Can I change my functional currency after I have filed returns?
It can change, but only because the underlying facts changed: a shift in where the entity earns and spends, a new funding structure, a different business. A change made for presentation, or because the numbers look better that way, is a different thing and will be read as one. Where a genuine change happens, the file has to be able to say which basis applied to which year and why the change date is the right one. Expect to keep both sets of translation working papers for the transition period, because the year of change is where the two bases meet and have to reconcile.
Which exchange rate do I use to translate my results?
The rule comes from the country whose return you are filing, not from the accounts. Broadly, amounts are translated on a basis tied to when the transaction occurred or to the period it relates to, and balances on a basis tied to the date they are measured at. What matters in practice is that the basis is stated, applied consistently across the whole computation, and used again the following year. Mixing bases within one return is what produces figures that cannot be reconciled either to the accounts or to the prior year, and that is usually harder to explain than the underlying position.
Does the reporting currency change how much tax I actually pay?
It can, and not only through presentation. Measuring results in one currency rather than another changes which items give rise to exchange differences, because an amount denominated in the functional currency creates none while the same amount in another currency does. So the choice determines whether certain gains and losses exist for tax purposes at all. That is why it is treated as a matter of fact and evidence rather than a formatting decision, and why the reasoning is documented. Two countries looking at the same entity can also measure it differently, and that mismatch is better identified before filing than after a query.
My accounts and my tax return want different currencies, what now?
You keep one set of books and translate them, rather than keeping two sets of books. The starting point is deciding what the entity's functional currency actually is, because that is the measurement basis. Presentation for a particular return is then a translation from it, on that country's stated rules. Where two countries each want their own presentation, both translations start from the same measured results, which is what allows the two returns to be reconciled to each other. Trouble almost always comes from translating a translation, so keep the working papers that show the route from the ledger to each return.
I work remotely from another country for a company back home — who taxes me?
Usually the country you are physically in, because employment income is generally sourced where the work is done, with your residence country taxing it as well if you are resident there and giving credit. Three things follow: your employer may acquire withholding and social security obligations where you sit, a treaty tie-breaker may be needed if both countries call you resident, and a short trip that becomes a long stay can cross a residence threshold nobody was watching. See remote workers and digital nomads.
How does a remittance actually work, and is it taxed?
A remittance is a transfer of money, not a category of income, and moving your own funds between your own accounts is not what creates tax. What can create tax is the income behind the money and the rules of the country it leaves. India, for instance, collects tax at source when a resident individual remits abroad under the Liberalised Remittance Scheme, and requires certification before certain payments leave. The transfer is the trigger for paperwork rather than for tax. See the LRS and tax collected at source.