I am thinking of visiting Beijing by End Dec and early Jan. Is it a good time for a tourist to come?

It is ok for tourist to China in Dec and Jan, but it is very cold in northern China, including Beijing. You need to bring warm cloths. If you are going to apply visa in Singapore, you can refer to application requirements from https://www.travelchinaguide.com/embassy/visa-application-singapore.htm please keep in mind that online appointment is required.