"Real time" hardly ever really exist in data analysis. What you could do is to schedule frequent reloads of your qlik app, and depending of the data quantity you probably want to look into how partial reload works if you reloading very frequently.
As for pulling data from API:s with qlik: sure, a simple answer is that you can. There are various connectors, including a general rest api connector. But it's hard to give more specific advice with such a general question.
