Can p-trap be installed higher than drain entry?
As long as the p-trap is lower than the drainage from the basin then you can install it. It can also be lower than your exit pipe you need to drain into 
You attach the p-trap directly to the drainage and manuever the p-traps exits into you existing drain.
It is not ideal to have the p-trap below the the exit drain because water gravity has to force the water out instead of it flowing downwards naturally. They both work and have seen it many times. But essentially anything below already creates its own p-trap- so using another is redundant.
If the p-trap is to tricky just create your own loop from pvc
For ease of manageability you can use a flexible waste connector pipe from the p-trap to your drain pipe.



Some twisted to fit p-trap



Small pcv p-trap





A sideways p-trap is useless, you might as well connect it straight line.



Theory of a p-trap



You might want to look into s-traps also