Evaluating the LightFM Recommendation Model

I've been playing around with lightfm for quite some time and found it really useful to generate recommendations. However, there are two main questions that I would like to know.

1. to evaluate the LightFM model in case where the rank of the recommendations matter, should I rely more on precision@k or other provided evaluation metrics such as AUC score? in what cases should I focus on improving my precision@k compared to other metrics? or maybe are they highly correlated? which means if I manage to improve my precision@k score, the other metrics would follow, am I correct?

2. how would you interpret if a model that trained using WARP loss function has a score 0.089 for precision@5 ? AFAIK, Precision at 5 tells me what proportion of the top 5 results are positives/relevant. which means I would get 0 precision@5 if my predictions could not make it to top 5 or I will get 0.2 if I got only one predictions correct in the top 5. But I cannot interpret what 0.0xx means for precision@n

Thanks