Learn French: Est-ce que les porte-manteaux et les micro-ondes sont déjà là ? - Are the coat racks and the microwaves already there?

Porte-manteaux is a compound noun made of a verb (porter) and a noun (manteau). In French, the verb part of a compound noun is invariable, meaning it never changes. Only the noun part takes the plural marker, which for words ending in -eau is an x.

Is les micro-ondes pluralized using the same rule as les porte-manteaux?

Not quite. While both are compound nouns, micro-ondes is made of a prefix (micro-) and a noun (ondes). Invariable words like prefixes never take a plural s, so only the noun part changes.

What would the singular form of les micro-ondes be?

It is exactly the same: un micro-ondes. Because the appliance uses multiple waves to heat food, the noun ondes always keeps its s, even when you are talking about just one single microwave!

Could we use inversion here instead of Est-ce que to ask the question?

You could, but it sounds very heavy. Because the subject is made of two long nouns, complex inversion is required: Les porte-manteaux et les micro-ondes sont-ils déjà là ? Using Est-ce que is much more natural and common in this situation.