Learn Portuguese (Portugal): O chefe ameaçou cancelar o projeto. - The boss threatened to cancel the project.

In Portuguese, the verb ameaçar (to threaten) connects directly to the following infinitive when expressing what someone threatened to do. You don't need a linking preposition like a or de here, even though English uses the word "to".

I've seen the word for "project" spelled as projecto. Is projeto the correct spelling in Portugal?

Yes, projeto is now the only correct spelling in Portugal. Under the modern Orthographic Agreement, silent consonants were dropped. However, the pronunciation hasn't changed: the e in projeto is still pronounced with an open vowel sound (like in the English word "pet"), which is what that old silent c used to indicate.

How would I add an extreme condition like "even if we protested" to this sentence using nem que?

You would use nem que (even if) followed by the Imperfect Subjunctive: O chefe ameaçou cancelar o projeto, nem que protestássemos. Because the main verb (ameaçou) is in a past tense, the hypothetical condition triggered by nem que must also be in the past (Imperfect Subjunctive).

Why is ameaçou in the Pretérito Perfeito (simple past) rather than the Imperfeito (imperfect)?