So I chose all the objects I don`t want to be rendered and changed their visibility, and then rendered the object I want, but it looks different while being isolated. Can I render it like if there are all other objects in a scene providing different types of reflections and so? Cycles.
You could use the Indirect Only restriction toggle option. It's only available for a whole collection. If you enable it, it will hide all the collection's objects but they will still affect the rendered ones.
Or select an object and disable its camera visibility in the Properties panel > Object > Visibility: