I wish I could be more specific.

If you need to move between T1 and T3 there is a security check en route. EY may have an additional security check at the gate. They may or may not allow your bottle of water. It depends on the airline and the current security stance.

BA make full use of the gate facilities (and at DXB, MCT, etc) and like to have the full theatrical production of shoes off, electronics out, everything swabbed, liquids confiscated, etc. QR tend not to do this.