B.Sc

Because you are not specific about the college, Hence the eligibility criteria of B.Sc. (Design - Interior and Furniture) [Lateral Entry] of LPU Jalandhar is given below. Eligibility criteria : Pass with 60% aggregate marks in Diploma (Interior Design or Architectural Assistantship or Civil engineering. ). [ (3 years after 10th) or (2 years/ 1 year after 10+2)] or equivalent. So from above you are eligible for B.Sc. Interior Design course of LPU. For more details please visit https://www.lpu.in/.

You can easily get admission in top colleges of Du. Colleges that provides B.Sc. Hons. Chemistry are
1. St. Stephen
2. Miranda House
3. Hindu College
4. Sri Venkateswara College
5. Ramjas college
6. Deen Dayal Upadhyay college
7. Kirori mal college
8. Deshbandhu college
And there are many other colleges that provides this course. Depending upon the college tuition fees may vary from 15000 to 35000. Hostel fees vary from college to college. For that you have to check the college website in which you are interested to take admission. Also check which college provides hostel facility or not on DU website.

Yes, you can have chances in 2nd or 3rd cutoff. Don't worry. For more details, check DU's previous year cutoff on DU portal.

There is no such information regarding the closed admissions for biotechnology. All the institutes are going for online admission process and many of the famous colleges in Mumbai have started taking up the entries.

Actually you can't do like this. If you have Masters in maths then cannot go for Ph.D. in Physics without Masters in physics. Similarly you should have maths as core subject to do M.Sc. in maths. Chemistry honours students cannot do maths honours if they don't have maths.