The issue of cultural diversity and therapy has certainly come to the forefront of importance in the last ten years. Part of this is the more universal acceptance of counseling as a medical and health related issue, rather than simply for those who are "emotionally ill".
Due to this more general acceptance, larger numbers of people have entered into counseling and are receiving psychological support. And the more this has occurred, the more the previous "one size fits all" approach to counseling has been forced to be re-evaluated. Even CBT, the primary clinical intervention method of counseling has been shown to be limited by cultural values. As a result, emotive and family based techniques have been combined with CBT techniques to make counseling more effective for a diverse population.
No matter the approach, some cultures still place stigmas on mental health treatment. Asian cultures, Latino, and some European cultures have strong (and often negative) opinions about psychological assistance. Even men are statistically much more resistant to therapy than women, and some cultures place significant stigmas on anyone who takes medications for a mental health condition.
As far as the second part of the question, there is no such thing as a culture fair test or assessment. This fact first surfaced in IQ testing in the early 1900's and still persists today in personality assessments, anxiety scales and measures of social interest.. No single test or assessment can account for variables in how a culture's norms may impact the client.
For example: Native Americans frequently test low on social and intelligence issues involving independent thinking and action. Their scores seem to indicate that they are "lazy" compared to many other groups in terms of autonomy, drive and independence. Yet, when interviewed in detail, the examiners discovered that the assessment questions appeared biased because the Native Americans who took the test naturally seemed to minimize group decision making and family values over individual goals because of culture.
Even diagnostics are not exempt from cultural issues. Clinically some disorders appear culturally biased. As another example: many cultures discount the western concept of oppositional defiant disorder in children, instead, referring to the disorder as "bad western parenting skills".
As far as misuse of assessment tools, a famous example in the U.S. is the MMPI, a test that evaluates abnormal behavior. A psychologist was hired to administer the exam to a group of potential used car salesmen. The test was used to screen for individuals who had the ability to lie without feeling badly about it, yet function well enough as sales people.
Group work is notoriously unfair to certain cultures who believe that emotional issues are very private, as well as martial counseling where partners are seen separately. In some cultures, for example Asian cultures, separating a marital couple for any reason is seen as wrong. Yet, both of these therapeutic techniques are widely used.
Each individual culture needs to be treated separating, according to their beliefs when treated in a therapeutic, research or assessment situation. It is difficult to impossible to create a tool or technique that can address the diversity of each culture in a fair and non biased manner.