Will I be able to see the Leonid Meteor Shower during mid night? Most of the articles online say that the peak will be in a couple of days and around 2:00 AM in the night. I am currently living in Dubai, UAE.

When I use Google Sky Maps, it shows both the Leonids Meteor Shower and Leo Constellation below the horizon, when using the search feature. It only comes above the horizon at around 6:00 AM, when it is 45 minutes since sun rise.

So, I am not sure whether it'd be dark enough to see them. What is my best course of action.

EDIT:
This link: https://www.timeanddate.com/astronomy/meteor-shower/leonids.html shows Leonids will appear at 65° Azimuth and 1.7° altitude. How'd I interpret that?
Leo starts to rise at about midnight, local time, so you should be fine, weather permitting.  Note also that you may be able to see meteors even before then, as Leo is merely that part of the sky from which the meteors appear to originate, but you will likely be able to see them some distance away from Leo.

I don't know where the Google rise time comes from.

EDIT; the link you added shows Leo rising at about midnight, confirming that the google source is incorrect, or not being correctly interpreted.