For History, you have to do BA in History and not BSc in History. As for the eligibility, yes science students are eligible for BA in History. Most colleges conduct merit-based admissions so make sure your 12th score is good enough. Some colleges even conduct entrance exams to shortlist the students for which you will have to prepare beforehand. Most top colleges accept marks higher than 85%.
No, it’s not possible to take lateral admission in a BA degree after completing a Civil Engineering diploma, in IDOL, YCMOU, or IGNOU. These two degrees are fundamentally different. You can get admission to BA after completing the course. But direct entry to second year isn’t possible.
IGNOU offers direct admission to some of its degree programs. For example, if you have done your BCA from IGNOU, you can join their 2 year MCA program through lateral admission. So, IGNOU lateral entry has fixed eligibility criteria. You won’t be eligible for direct admission to second year in IGNOU MCA if you completed your BCA from any other university.