Why are these words written similarly? Do they descend from a common Chinese character? If so, how do you explain the difference in pronunciations among derived words, especially for 戎?
投笔从戎 róng 盗贼 zéi 绒毛 róng
The characters resemble each other because 「戒」 was subject to a slight amount of structural shuffling and the original lower-left component of 「戎」 is of a simple shape, so most people won't recognise what it actually is.
As far as I can recall, the only other place that the lower-left component of 「戎」 occurs in is the top of 「古」.
「戒」 and 「戎」 aren't the same character, they don't descend from the same character, and the morphemes they represent aren't related (except in the sense of semantics - both are pictographs containing 「戈」, dagger-axe).
It follows that they sound completely different, whether as individual characters or as part of a phonetic hint function in other characters.
「戒」 depicts two hands 「廾」 holding up a dagger-axe 「戈」, indicating the meaning to warn/caution. 「廾」 later migrated to the lower-left of the character and no longer appears to be holding up the weapon anymore; the structural analogy to the original form is 「𢌵」.
「戎」 depicts a dagger-axe 「戈」 together with a shield, indicating the meaning armaments.
Shield is now written as 「盾」. The original character doesn't exist individually anymore, but remains as the top component of 「古」 (solid, sturdy, now written as 「固」).
This character was later replaced by the new character 「盾」, which depicts a side view of the shield with an eye looking straight 「直」 peering from underneath the cover of the shield.
As for 「賊」, it doesn't actually contain 「戎」. 「賊」 (Baxter-Sagart OC: /*k.dzˤək/, to ruin/damage/destroy) is comprised of semantic 「戈」 (dagger-axe) and phonetic 「則」 (/*[ts]ˤək/). The 「刂」 part was later corrupted into a 「𠂇」 shape, causing the right hand side of 「賊」 to be misinterpreted as 「戎」.
As for the auxiliary question, why 贼 is pronounced so differently to 戎 / 绒, that's because 贼's phonetic component is not on the right hand side, but kind of on the left hand side.
Although modern 賊 is written as ⿰貝戎, in the Bronze Script it was ⿹戈則, where 則 is the phonetic. The phonetic correspondences are thus not too bad: