Q:

Is it a good idea to improve my writing skills by "fixing" what others wrote? 

So, I tried out a new thing.  Take this segment from The Eye of Argon:

The weather beaten trail wound ahead into the dust racked 
  climes of the baren land which dominates large portions of the 
  Norgolian empire.   Age worn hoof prints smothered by the sifting 
  sands of time shone dully against the dust splattered crust of 
  earth.   The tireless sun cast its parching rays of incandescense 
  from overhead, half way through its daily revolution.   Small 
  rodents scampered about, occupying themselves in the daily 
  accomplishments of their dismal lives.   Dust sprayed over three 
  heaving mounts in blinding clouds, while they bore the burdonsome 
  cargoes of their struggling overseers. 
       "Prepare to embrace your creators in the stygian haunts of 
  hell, barbarian", gasped the first soldier. 
       "Only after you have kissed the fleeting stead of death, 
  wretch!"  returned Grignr. 
       A sweeping blade of flashing steel riveted from the massive 
  barbarians hide enameled shield as his rippling right arm thrust 
  forth, sending a steel shod blade to the hilt into the soldiers 
  vital organs.   The disemboweled mercenary crumpled from his 
  saddle and sank to the clouded sward, sprinkling the parched dust 
  with crimson droplets of escaping life fluid. 
       The enthused barbarian swilveled about, his shock of fiery 
  red hair tossing robustly in the humid air currents as he faced 
  the attack of the defeated soldier's fellow in arms. 

This is already a good passage; let's make it even better:

The weather beaten trail wound ahead into the barren land which dominated most of the Norgolian empire.  Old hoof prints smothered by the winds shone dully against the dust-covered earth.  The sun sat high, casting its parching rays down below to the dismay of the small rodents that scampered about. 
Blinding clouds of dust sprayed over three horses, heaving under the
  weight of their riders. 
"Prepare to embrace your creators in the stygian haunts of hell,
  barbarian", shouted the first soldier as he caught up to the barbarian, sword raised. 
"Only after you have kissed the fleeting stead of death, wretch!" 
  returned Grignr.  A flash of light swept across the rivets of his
  hide-enameled shield, as the barbarian's rippling right arm
  thrust forth, sending the steel sword through the chainmail, hilt-deep into the soldier's
  belly.  The soldier's eyes widened.  Grignr tightened his grip and yanked the sword out, slashing his opponent's side open. 
The disemboweled soldier crumpled from his saddle and fell on the
  clouded sward, sprinkling the dust with crimson droplets of blood.  A smile stretched across Grignr's face. 
The barbarian spun around, his fiery red hair tossing in the
  air currents as he raised his sword to block the other's. 

Note: I don't know enough bout horseback sword fighting (especially when both opponents are riding), nor do I know what equipment the soldiers have.  Also, sorry for the chainmail bit, I know it's bs. 
The basic idea is that I find issues and fix them, making me both a critic and a writer.  I can't say it's hot garbage, I have to methodically break down the reason why it's garbage, like failing to establish the position of the combatants in space and the redundant redundancy. 
That takes care of the critic, but then you have to "fix", which invariably involves writing and writing new ideas.  This new ideas usually morph the story in a way that's unique to most writers, developing their style. 
IN PAPER! 
While it is fun, I'm not sure.  Could this practice be detrimental to developing my own style?  I have to add and/or change stuff, but still...
Also, while you might not be able to wrap your head around it, but there are instances of books that, for one reason or another, weren't properly edited.  These range from the self-published "works" of Onision, to fan stories and borderline fan stories (The Eye of Argon, at least the version I used, was originally published in a sci-fi magazine back in 1970). 

A:

To be fair, I'd recommend that you solely work on your writing before you start to critique others, especially if these others are already published.  If they've published, they were likely already professionally edited.  Your works have not.  Perfect your own writing by reading aloud your work, and by giving it some rest.  By this, I mean allowing at least a month or two weeks before reading through it.  You have to read your work objectively.