Need some advice
 

That would still lie on your preferences. If you find it difficult to handle tri cockpit then I think it would be okay to change to the normal set up ones :) I also prefer the normal btw.

Besides fitting the bars of your choice, and a conventional brake lever shifter setup, (you are going to 'brifters?') You will more than likely need to replace the stem, as well.
I don't know much about the Equinox series or the E11, but it doesn't look to have too radical of geometry, which makes the conversion more straightforward.
It does have a short head tube, which is typical of tri-bikes; the aero cockpit sits 'on top' of the stem, and by design, puts the rider in to a low, flat aero position.

You will need a taller and possibly longer stem to put a set of drop bars at a conventional height, unless you want the 'full attack' position.
If you're having a shop do the conversion, you can get them to measure you out on some conventional road bikes, to help get the bar/ stem height to a good fit for you.