Difference between Theravada's self and Mahayana's intrinsic essence
1. Do other Mahayana Buddhists apart from the commentator above, also call the intrinsic essence (svabhava) of a chair, as the "self of chairs"?

Yes, this is a common expression in Mahayana texts on the topic.

2. If Theravada states "sabbe dhamma anatta" and Mahayana states "sabbe dhamma asvabhava", does it mean that anatta = asvabhava, and therefore, atta (self) = svabhava (intrinsic essence)?

I think Mahayana states "sabbe dhamma shunyata" - which can be explained as "sabbe dhamma asvabhavata" and "sabbe dhamma pratityasamutpida". From this it also follows that all dharmas are anicca (ephemeral) and dukkha (here, faulty/unreliable).

If we don't nitpick too much about the meaning of the equal sign, I think I can agree with your statements that "anatta = asvabhava" and "atta = svabhava". More on this in a second.

3. Depending on your view: if the Theravada atta (self) is different from the Mahayana svabhava (intrinsic essence), then what really is the difference? OR if the Theravada atta (self) is same as the Mahayana svabhava (intrinsic essence), then does that make the Mahayana emptiness a redundant concept?

I think svabhava is a broader concept than atman (atta). To me, atman is only one case of reification, or one case of attributing svabhava to abstractions and observations.

Therefore, Mahayana's emptiness is not redundant. True -- it is not something entirely new that was absent in Theravada, but in my opinion it gives proper emphasis to something that is kind of implicit and not explained enough in the Pali Canon (even if ever-present "between the lines").