Learn Farsi: برادر کوچکم به اندازه‌ی خواهرم لوس است، اما لجباز نیست. - My younger brother is as spoiled as my sister, but he is not stubborn.

به اندازه‌ی literally means 'to the size of' or 'to the extent of'. Farsi doesn't sandwich the adjective between two words like English does with 'as... as'. Instead, you place the entire comparison before the adjective. So the literal structure here is 'My younger brother to the extent of my sister spoiled is'.

Why is the possessive suffix -َم (my) attached to کوچک (small/young) instead of برادر (brother)?

Possessive suffixes always attach to the very end of a noun phrase. Since کوچک is an adjective describing برادر, they are linked by an ezâfe (برادرِ کوچک). The 'my' suffix must wait until the end of that descriptive phrase, resulting in برادر کوچکم.

Why is there a ی at the end of اندازه‌ی?

This is the ezâfe connecting اندازه (measure/extent) to the following noun, خواهرم (my sister). Because اندازه ends in a silent ه (h), the ezâfe requires a 'y' sound to bridge the gap smoothly, which is written here with the letter ی.

Do I need to include a subject pronoun like او (he) before لجباز نیست (is not stubborn)?

No, it is perfectly natural to leave it out. Because the subject of the first clause is clearly برادر کوچکم (my younger brother), Farsi simply carries that same subject over to the second clause without needing to repeat it with a pronoun.