1. gd_categories is designed to be responsive, but some improvements are needed to make it look better in tablet sizes, certainly. A task has been created to look into the issue and improve the display.
2. The instructions for conversion for the beta are available here: https://wpgeodirectory.com/docs-v2/geodirectory/installation/#convert
When the final v2 release is ready, there will also be an upgrade path with fewer steps.
This is a major version upgrade. We hope that the improvements in V2 make design faster and easier. In my experience so far this has been the case. Template projects for customizing the detail page that previously might have take a week now take only a day or two and are easier to maintain because they do not require code changes or php template modification.
When V2 is released then V1 will only receive security updates