Do scriptures prescribe how the yagynpavitam should be made (number of threads, knots etc.)?
Use of word "Caste" when talking about Hindu scriptures is very confusing. There are Varnas (based on gunas) and Jatis n gothras (based on bloodlines), caste as a concept doesn't exist in scriptures.
According to Agamas, yagnopavita is the same for all, it changes based on certain attributes depending on the level of consciousness for the people wearing it.
Shaiva Agamas describes how many threads an individual has to wear based on his/her Sadhana. Any one can be initiated in to wearing Yagopavitha provided the individual adheres to certain required practices.