Can I do Diploma and graduation at the same time? Like can I do Polytechnic and B.A. together?

Well, you can do a Diploma and graduation simultaneously. You can start a Diploma in any engineering course on a regular basis and pursue Graduation from some open universities like IGNOU it's completely valid but when you will apply for government jobs you can use only one Certificate as per my kno

Yes, you can do both at the same time You have to manage the time for both of the things and have to set priority to score well.