for the checklist places, if you just want to see them as a layer on a map (not do more complicated analysis), you should be able to load them as a XYZ layer. for example, if you want to see taxa 55387’s checklist, create an XYZ tile layer that references http://api.inaturalist.org/v1/taxon_places/55387/{z}/{x}/{y}.png. you can see the iNaturalist API documentation to see what other polygon tiles (api.inaturalist.org/v1/docs/#/Polygon_Tiles) and observation tiles (api.inaturalist.org/v1/docs/#/Observation_Tiles) you can get.
here’s an example where i pulled in a taxon range into a map using XYZ tiles: https://forum.inaturalist.org/t/ideas-for-heatmaps-displaying-abundance-of-observations-on-maps/5995/3.