An apostille is a single certificate accepted between countries that have both joined the Hague Apostille Convention. Legalisation is the older chain used when the destination has not joined: each authority certifies the signature of the one before it, ending at that country's own embassy or consulate.

Almost never. Nearly every mission requires the document to carry U.S. Department of State authentication first, which in turn requires state authentication for state-issued and notarised documents. Skipping a layer means the package comes back unlegalised.

The state that issued it. A birth certificate from Texas goes to the Texas Secretary of State even if you now live in Ohio. For notarised documents it is the state where the notary is commissioned.

Realistically three to ten weeks. The federal layer alone is about nine business days by drop-off or roughly five weeks by mail, and the embassy stage varies from two days to several weeks depending on the country.

Often, but usually not before legalisation. Most countries want the translation performed after the document arrives, by a translator their own ministry recognises. Translating first can mean paying twice.

The route changes on the entry-into-force date. Documents already legalised stay valid, but from that date an apostille is normally what the receiving authority wants. Practice can lag the treaty by weeks, so confirm with the receiving authority.