Learn Portuguese (Portugal): Vou ser implacável, custe o que custar.

This is a fixed concessive structure used to say 'no matter what' or 'whatever happens'. It combines the present subjunctive (custe), a relative phrase (o que), and the future subjunctive of the same verb (custar). Literally, it translates to 'may it cost what it will cost'.

Isn't custar just the infinitive? How do I know it is the future subjunctive here?

For regular verbs like custar, the future subjunctive looks exactly the same as the infinitive. However, the rule for this specific structure requires the future subjunctive for the second verb. You can see this clearly when using irregular verbs, such as diga o que disser (whatever they say), where the future subjunctive disser is very different from the infinitive dizer.

Can I use this structure to talk about the past, like 'whatever it cost'?

Yes! To shift this to the past, you change both verbs to the imperfect subjunctive. So, 'whatever it cost' becomes custasse o que custasse.

Is implacável commonly used in Portuguese, or is it a formal word like 'implacable' in English?

While it is a direct cognate to the English 'implacable', implacável is much more common in everyday Portuguese. It is the standard way to say someone is 'relentless', 'ruthless', or 'unforgiving' in their actions.