Is there a Chinese variant of the expression "and the list goes on and on" or something simillar to it?
There might be many expressions in different cases. The most common one should be:
等 or 等等： etc.; and so on
Outside of the common 等等, it seems like 诸如此类 and 诸如...之类 match your request. Native speakers, please correct me if I'm wrong.
There's a 成语 expressing this meaning：不胜枚举