Is there a formal name for the compulsive and recurrent urges to pick one's nose in order to remove perceived imperfections? Under which formal category does the following condition fall?: the condition of experiencing frequent and compulsive urges to pick one's nose searching for any possible perceived imperfections (be they wet snot, dry snot and even scabs) in order to remove them or "smooth them out" by means of scratching, in a sort of endless pursuit for a sensation of perfect smoothness within one's nose (endless because the sensation of perfect smoothness is never quite achieved and usually the scratching itself leads to bleeding and scabs which paradoxically become the fuel for future nose picking sessions, in an endless cycle). Likewise, are there any formal treatments to cure this particular condition? How effective are these treatments? Are there any studies on this? References are very welcomed.
Excoriation disorder (ED) formerly known as dermatillomania, and more popularly as Skin Picking Disorder (SPD): 


  a mental disorder characterized by the repeated urge to pick at one's own skin, often to the extent that damage is caused.


The status as a separate disorder is somewhat controversial, because of high comorbidity:


  There has been controversy over the creation of a separate category in the DSM-5 for excoriation (skin picking) disorder. Two of the main reasons for objecting to the inclusion of excoriation disorder in the DSM-5 are: (1) that excoriation disorder may just be a symptom of a different underlying disorder, e.g. OCD or BDD, and (2) that excoriation disorder is merely a bad habit and that by allowing this disorder to obtain its own separate category it would force the DSM to include a wide array of bad habits as separate syndromes, e.g., nail biting and nose-picking.


Your case seems to be one of those overlapping ones.

There's also a 2017 neuroimaging study which concludes:


  data offer partial support for the view that sub-cortical structures contribute to the pathophysiology of SPD, both supporting its categorization as an OC-Related Disorder in DSM-5 and suggesting that there exists a pathophysiological difference between SPD and OCD.


Wikipedia has a lot to say about various treatments even though


  Knowledge about effective treatments for excoriation disorder is sparse despite the prevalence of the condition.


The usual suspects have been tried: SSRIs, anti-psychotics, anticonvulsants, glutamatergic agents (used to treat drug addictions) etc. As well cognitive-behavioral psychotherapies. It's not clear from there what might be most effective.

Wikipedia aside, there's been a "preliminary meta-analysis" published in 2014, but its review at CRD notes:


  Authors' conclusions:
  Both pharmacological and psychological interventions appeared to be effective in reducing the severity of pathological skin picking; psychological interventions could have a larger effect.
  
  CRD commentary:
  The authors did not report a quality assessment, so it is difficult to know how reliable the results of the individual studies were. Many of the studies had designs prone to bias. Details about the comparator interventions, in the studies with control groups, were not reported. Given the heterogeneity across the studies, the limited reporting of study details and the unknown quality of the included studies, it seems inappropriate that the results were statistically synthesised, particularly for pharmacological and psychological interventions, for pathological skin-picking severity.


So I wouldn't put too much stock on it.

A more recent (2016) meta-analysis has basically the same conclusions; this one was not reviewed at CRD, but it relies basically on the same small number of studies. Its conclusions were similar to the "preliminary" one: psychotherapy seems to work better than medication based on the limited data available. It only looked at SSRIs and lamictal for medication though.

There's also a 2016 RCT on N-acetylcysteine, published in a high-impact journal, concluding:


  N-acetylcysteine [NAC] treatment resulted in significant reductions in skin-picking symptoms and was well tolerated. 


The result was fairly unsurprising given that NAC was previously found effective for trichotillomania (TTM -- hair pulling) as well; both studies with NAC were conducted by the same research group. But there were a few more interesting comments on those papers:


  In striking contrast with what we know about OCD, SSRIs
  have not been proved to be superior to placebo in TTM
  treatment. As for ED, the evidence regarding the efficacy of
  SSRIs is still scarce. So far, there are no US Food and Drug
  Administration–approved treatments for ED and TTM. The
  divergent results of the trials testing either SSRIs or NAC for
  ED/TTM and OCD suggest that treatments may not be used interchangeably
  between OCD and related disorders.
  
  In addition, results from genetic studies also suggest
  that the neurobiology of pathological grooming may not be
  necessarily related to OCD. It had been demonstrated that
  Sapap3 knockout mice groomed themselves excessively.
  However, using family-based association analyses, Bienvenu
  et al found that variation within the human equivalent of
  the Sapap3 gene appeared associated with ED/TTM, but not
  with OCD.
  The conflicting results regarding the efficacy of NAC for
  ED/TTM and OCD, in addition to the findings of translational
  studies, suggest that the neural basis of repetitive behaviors
  observed in patients with these disorders might not be the
  same. So far, similarities between ED/TTM and OCD do not
  seem to go beyond the characterization by repetitive behaviors
  and some degree of familial aggregation.


(But note that this last statement appears somewhat incorrect in view of the 2017 neuroimaging study--some overlap with OCD seems to exist after all.)

NHS Choices also has consumer-oriented page on "Skin picking disorder
" which doesn't say much I haven't told you already except for some behavioral tips. YMMV.