FP-Growth and Association Rules

I have recently worked through this video and created a dummy dataset, Fp-tree and conditional database. I have two questions regarding the outputs:

1. Are these example outputs correct given the inputs?
2. Are association rules generated by utilising the frequent patterns found?
3. If yes to 2, is there almost a 'skip-level' association in play? For example, for the Carrots patterns. I can see the flow is Beer - Diaper - Carrots. But could a frequent pattern be also Diaper - Carrots and Beer - Carrots, as the pattern could skip the intermediary and/or preceding nodes?

Inputs Let minimum support = 0

Outputs FP-tree

Conditional Patterns View