Well instead of minor parties, there are simply different factions in both the CPC (the executive branch) as well as the People's Congress. Although there are actually minor parties in the National People's Congress, but even to me they seem like tokens.

There are more hardline Leninists vs more free market liberals, among other stances for the way China should move forward in both branches. Nanjie, for example is still Maoist because the people chose leadership to remain Maoist, compared to Shenzhen or Shanghai which is far more liberal. Although as a whole, in recent years "centrists" (by Chinese standards) have been more likely to be elected upwards beyond a regional/county level, but that might be due to the fact that the status quo, although not perfect, has been more beneficial than detrimental to the average Chinese.

As far as I'm aware, the lowest levels of election would be the equivalent of like a village council (although villages in China may be considered a small city in other countries), and candidates I believe have to be citizens that have no prior convictions. Relevant background also helps.