Is it possible to create a new starting point/airport with latitude/longitude?
All you need to do is go to where you want to start, then click 'save flight' on the 'Flights' menu.
In that area should be a box which says 'Make default flight' make sure that box has a tick in it and then the next time you start FS it should have that flight loaded in the Create a Flight screen, so you can go straight there!
I think thats how it works anyway! If it doesnt, then go to select flight from the main screen, then find your saved flight and tick the box which says make default flight.
If you're asking how to move the aircraft to a specific latitude/longitude, you can do that in the "Map." Start a flight, click the Map icon on the instrument panel (looks like a star, actually a compass rose) and enter the lat/long position you want into the windows on the left. When you click okay, your plane will be moved to that position. For instance, I just opened a flight in Alaska, entered lat/long of 0 deg/ 0 deg, and found myself floating in the ocean off the west coast of Africa, on the equator and the prime meridian. Fortunately, I was in an amphious plane!
As far as creating an airport at that location, there are add-on programs for doing that, but I have no experience.