Panjab University

Yes, you can get B.Sc(Hons.) maths if you have filled PCM.

There is no requirement of any professional course for become an actor but if you want you can join acting school and also can do graduation in B.A. Acting and if your graduation was complete, then you can also go for Masters in acting this courses will help you to finishing your skills.

For this, you can contact to the college authority directly as in my knowledge there is no such provision of getting directly in to the 2nd year of BCA in this university.

Hello Rounak,
It is very nice to hear from you that you are interested in doing your engineering from Punjab University located in Chandigarh. It's quite well known in Punjab and whole of North India as an institute of repute. I am attaching a link that will give you all the required information about different aspects of the admission process for different courses in this university. https://www.shiksha.com/university/panjab-university-Chandigarh-4026/admission
Best wishes to you.

You can get resources online from Google and YouTube. You can prefer BCA entrance book by Arihant publications, it covers almost all the topics from the entrance point of view.
Good luck.

Punjab University does not offer MCA lateral entry.
Good luck.

The PU- CET is open and can see details on http://admissions.puchd.ac.in/includes/admissions/2019/20190408153747-cetugposter2.pdf
The Panjab University Bachelor degree course notice for admission is on the above link with all details. You can also seek enquiry on the numbers mentioned below:
1800-180-2065, 2534866 (from 9:30 am to 1:00 pm & 2:30 pm to 5:00 pm on working days including Saturday).