Learn Italian: In questa salumeria vendono dell'ottima mortadella. - In this delicatessen they sell some excellent mortadella.

The partitive article must agree phonetically with the word immediately following it, not just the noun it modifies. Because the adjective ottima starts with a vowel, the feminine partitive della drops its final vowel and takes an apostrophe, becoming dell'.

Is it mandatory to use dell' here, or could I just say vendono ottima mortadella?

You can leave it out! In Italian, it is grammatically correct to omit the article when talking about an indefinite quantity of an uncountable noun (like meat or water). However, adding the partitive article to mean "some" is extremely common and often sounds more natural in everyday spoken Italian.

Why is the adjective ottima placed before mortadella instead of after?

While most descriptive adjectives go after the noun, those expressing subjective value or goodness (like buono or cattivo) often go before it. Ottimo is the absolute superlative of buono (meaning "excellent" or "extremely good"), so it follows the same pattern and is placed in front of the noun for emphasis.

Who is the subject of vendono if nobody specific is mentioned?

This is an impersonal use of the third-person plural. Italian frequently uses the "they" form to refer to "people in general" or "the staff" at a business, very similar to how we use "they sell" or "they say" in English.