The hose and gauge are stored within the pump itself. You can access this by lifting the cap at the handle end of the pump and pulling out the hose within. You then screw the relevant end of the hose into the body of the pump and it is then ready to use.
The frame of your bicycle will need pre-drilled holes in the frame, and there should be bolts screwed into these holes. To install the bracket, ensure the threads on the mounting bolts are clean of debris, paint and metal chips, and then put a thin film of grease on them. You then line up the bracket with the holes, and hand tighten the bolts using a screwdriver or allan key, whichever is relevant. Be careful not to cross thread the bolts!
Yes, however you will need to ensure that the removable element is fully screwed into the valve so that it does not twist and come loose when you screw the pump hose onto the valve. If this does not work, you could also consider superglueing the core into the valve.
You need to ensure that the Presta valves are fully open, and then screw the hose valve head DEEPLY onto the tyre valve. This creates a full seal, allowing all the air to be pushed through when pumping. If a full seal is not created, then the air will sometimes get trapped in the pump. This will cause a ‘backup’ of air making pumping difficult, and in some cases the pump will heat up as the air has nowhere to go.