Learn German: Nach dem Gespräch war alles gut. - After the conversation everything was fine.

The temporal preposition nach (after) always takes the dative case. Because Gespräch is a neuter noun (das Gespräch), the word for "the" changes to dem in the dative.

Why is the verb war placed before the subject alles?

This is the classic German "verb second" rule in action. The time phrase Nach dem Gespräch takes up the entire first position of the sentence. To keep the verb in the second position, war has to come next, pushing the subject alles into the third position.

Does nach always mean "after"? I thought it meant "to", like in nach Deutschland.

It means both, depending on the context! When you use nach with a time expression or an event (like a conversation or a meal), it means "after". When you use it with cities, most countries, or directions, it means "to".

Why does alles take the singular verb war?

The word alles is a pronoun meaning "everything". Just like in English, "everything" is treated as a single concept, so it takes the third-person singular verb form war (was) rather than a plural form.