My question is, "When will the Tesla Coil patent expire?", What year will it expire?, how soon? and after it expires, will anyone have access to mimick the invention?
This patent was issued January 9th of 1894. Back then, I believe US patents lasted for 17 years from their grant date so it should have expired January 9th of 1911 (more than 100 years ago). Since 1995, US patents expire 20 years after their filing or priority date.
Once a patent expires, anyone can use the technology described in it. This is the basic premise of patents. In return for teaching the world about a new technology, you get a limited term of exclusivity. You always need to be aware, that there is the potential for other relevant patents such as refinements to the original so a patent search is often a good idea.