Economics

Himalayan University offers Ph.D programme in full-time and part-time mode only. M.Phil is not offered.

Yes, there will be entrance for UG in economics and as per the sources say the online registration will be start in 2nd week of June 2018 and may close in 4th week of June 2018. and for syllabus, you may solve previous year question paper or you must have knowledge of the following topics:-
microeconomic theory, macroeconomic theory, mathematical techniques used by economists, and probability, statistics and elementary econometrics.
Best of luck.

https://www.shiksha.com/careers/economist-39
I think this would be helpful for you.

Where are you planning to apply and also which exam are you giving?

No, it's not mandatory to have maths in best four but you need to have maths as one of your subjects in +2. Although, it is mandatory to have economics (without which a deduction of 2.5% will be done) and English ( or other language subject). Hope this helps.

SNUSAT Question & Sample Papers 2018:
Download previous year question papers and sample papers of SNUSAT 2018 for your exam practice at the link provided below. You can download all last years' SNUSAT exam question papers and sample papers free of cost. You can also download preparation guides for SNUSAT designed by Shiksha experts. https://www.shiksha.com/university/shiv-nadar-university/exams/snusat/question-papers.

BA in economics deals with other fields of economics, as in macro micro, so it is much tougher than BA. On the other hand, BA only offer little bit of economics, which is really less as compared to BA in economics.

Proper date is still not announced.

You can get the previous year entrance question paper in the link mentioned https://www.shiksha.com/university/kurukshetra-university/exams/kuk-entrance-exam/question-papers.