Do you think that H index reflect experience?

Somewhat. Generally, researchers with more years of experience tend to have higher H-indices, as they have had more time to publish and get citations. But this correlation is far from perfect. 

I think yes because H-index can reflect the interesting of other researchers to read and benefit from published manuscripts.  

he H index is an important measure of a person's contribution to the scientific literature. However, the H index alone does not provide sufficient evidence about a person's success. The H index is a metric that combines the number of publications and the number of citations received by an author. It has been used to evaluate research performance at the institutional level as well. While the H index is a useful metric, it has some limitations. For example, the H index does not take into account the quality or impact of the publications, only the quantity. To address this limitation, researchers have proposed new metrics such as the influence-primed H index, which weights citations by how many times a reference is mentioned in the citing paper.

It is basically a function of the number of papers published irrespective of their quality. So in a way, it is directly related to "experience"...

I do not because the pressure to publish has increased last years. The quality and the true expertise of the researchers it is not well reflected in the number of publications and citations. Hence, it's more related to the quality of your contact list and friends across the academic world. Just my personal opinion.

I do believe so, as it directly related to the years since first publication