Learn Arabic (Modern Standard): اشترى المدير أحدث هاتف أزرق. - The manager bought the newest blue phone.

Because superlatives using the أفعل pattern create an Idafa (possession) structure. Instead of acting like a normal descriptive adjective, أحدث acts as the first word in the Idafa, followed by the noun it describes.

If the English translation says 'the newest', why doesn't أحدث have the definite article ال?

Because it is the first word in an Idafa construction. A strict rule of Idafa is that the first word can never take ال, even if the meaning in English includes the word 'the'.

Why does the regular adjective أزرق (blue) come at the very end?

Unlike the superlative أحدث, the word أزرق is a regular descriptive adjective describing the phone. Regular adjectives must always follow the noun they describe, so it comes right after هاتف.

Can I say المدير اشترى instead of اشترى المدير?

Yes, you can. However, Arabic generally prefers to start sentences with the verb. This is called a verbal sentence and is the most standard word order in Modern Standard Arabic.