한국은 과거엔 구한국인 대한제국과 구별하여 신한국이라고도 불리기도 했다. = Korea at one point was also called the new Korea as distinguished from The Empire of Korea which was the old Korea. 1. 구한국인 대한제국 = The Empire of Korea which is/was the old Korea. 이다 means "is" (linking verb). So 대한제국은 구한국이다 means "대한제국 is the old Korea". We can create a noun phrase around 대한제국, like so: 구한국인 대한제국 (대한제국 which is the old Korea). 인 is 이(다) conjugated with -ㄴ, a suffix creating a present tense attributive adjective. 2. 구별하여 = 구별하여서 = 구별하다 (distinguish) + -아/어서 (verb ending giving a reason, means, or background). 3. 불리기도 한다 means "is also called", as contrasted with 불리다, "is called". 불리다 is the base verb form. 불리기 is its noun form, and 도 adds the sense of "also" or "as well". It's best to understand -기도 한다 as an idiom for "is/does also ...".