Can I (an Indian National) travel with Chinese single entry tourist visa to Shenzhen as well as Beijing in a single trip? Like, Bangalore (India) to Shenzhen, then stay in Shenzhen for two days, then from Shenzhen to Beijing and then stay there for some days, and then back to Bangalore (India) from Beijing. Or do I need a sepearte Shenzhen visa?
You can do that.
You have a single-entry visa from China. That visa allows you to enter China one time. Both Shenzen and Bejing are in China. Your trip, therefore, is a single entry into China, some traveling between Shenzen and Beijing within China, then exiting China to return to India.
A visa on arrival for Shenzen only can be obtained for travelers who are going to Shenzen by land from Hong Kong, but that doesn't apply to you as you have a regular visa.