Does a political party based on a minor (or major) ethnicity have a place in democracy ?
In my opinion Yes absolutely however it can be sign of deep social and cultural turmoil when this starts to occur on a large scale.
Political parties should form around a common set of beliefs, and if a particular minority ethnicity in a nation feels that its people are not being represented well or that this ethnicities values are going unheard then forming an ethnic party becomes a healthy democratic outlet for government activism. This is much preferable to the alternative of ethnic minorities being ignored or shunned from politics, or for revolts, terrorism or full scale civil war to occur.
Because ethnic minorities are a minority by overall population, ethnic parties around minority groups generally must form coalitions with other minority parties that they share some similarities with to gain any type of meaningful power in the parliamentary system. This encourages other ethnic parties as well as tradtitional parties to work closely and compromise with one another to achieve common goals. This collaboration encourages good relations between different ethnicities in the same country.
Are Ethnic Parties preferred? Probably not. The best political party is one that is not exclusive based on race, creed, ethnicity, gender or sexual orientation but then it is not always possible for an ethnic minority to be accurately represented in any other way. It should be worrisome that minority groups feel that certain elements of the society or culture exclude them or do not closely represent them in any meaningful way. The most worrisome would be if an ethnic party formed around the majority ethnicity as this can spell Majority Tyranny against minority groups in the country.
Based on the cultural makeup of the citizenry however, ethnic parties can make sense in the democratic process.
Depends on what you mean by "have a place". In a true liberal democracy, people have freedom to associate by any principle they want, including the principle of belonging to a specific ethnicity, religion, ideology, sexual preferences or soccer team tastes.
However, if such party would advocate preferential treatment of certain ethnicity by the state, it should not be allowed to turn this advocacy into the law. The easiest way of doing this is to avoid electing such people into power and generally shunning them and shaming them out of the political scene. However, it is virtually impossible to ensure such party would not be able to prevail - ultimately, the people are the sovereign, so if most of the people want it, it will happen one way or another. However, such actions - i.e. preference of certain ethnicity by the state - are definitely incompatible with the modern democracy. Thus, for citizens that value the modern democracy it is prudent to avoid such parties by all means and ensure they never have a chance to gain any power.
Fortunately, in most current liberal democracies ethnic parties are mostly bothered with, in the best case, preventing ethnic discrimination, and in the worst case - trading votes for the parts of the budget directed to the projects they see to disproportionally benefit their ethnicity. As such, they do not pose much danger to the democracy.