They are both conjunctions - definitely not prepositions. I wouldn't call 'and when' a conjunctive phrase, though, because these two words are independent of each other and serve different purposes.
The 'and' is a coordinating conjunction linking the two halves of the sentence; the 'when' is a subordinating conjunction relating only to the second half. They just happen to be next to each other in the sentence.
By the way, I just wanted to say 'good on you', as a native English speaker, for asking questions about English grammar.
There are many native English speakers here who don't admit to the gaps in their grammatical knowledge of the language, and they use terminology wrongly and give inaccurate and misleading explanations to foreign learners. Even if their intentions are well-meaning, such people do more harm than good. So I think that it's great that you're asking about things that you're not sure of. There'll usually be someone here to help if you have any queries.