Learn Russian: Какой это размер?

Какой means 'what' or 'which'. It acts like an adjective, so it must match the gender of the noun it asks about. Because размер (size) ends in a consonant, it is a masculine noun. Therefore, we use the masculine form Какой.

If размер is masculine, why do we use это instead of the masculine этот?

In this sentence, это is used as a standalone pronoun meaning 'this is' or 'it is'. When used this way, it always stays as это, regardless of the noun's gender. You would only use the masculine этот if it was grouped directly with the noun to mean 'this size' (этот размер).

Where is the verb 'is' in this sentence?

Russian leaves out the verb 'to be' in the present tense. Literally, this sentence is just 'Which this size?', but it translates smoothly to 'What size is this?'.

How would I change this sentence to ask about plural sizes, like 'What sizes are these?'?

To make this plural, you change the question word and the noun to their nominative plural forms. Какой becomes Какие, and размер becomes размеры. The pronoun это stays exactly the same when it means 'these are'. So the plural sentence is Какие это размеры?.