Depending on your industry the answer can be different, but I'll take a stab at it.
Pipe & tube are nearly synonymous or you could argue that pipe is a subset of tube. Pipe normally has looser tolerances, is always round, is normally pressure containing, is either seamless or welded, and is usually available in standard sizing (see API Spec 5L or ASME B36.10. Tube on the otherhand is available in virtually every shape, size, and material.
In the oilfield a string is the casing or tubing that is suspended in a wellbore. The flowline is the pipe that runs from a wellhead to your gathering facillity or pipeline.
I can only answer the pipe/tube query.
In industry usually the difference refers to the dimension that you are describing. Pipe specifies the inside diameter of the material, e.g. 1/2" Pipe has 1/2" ID yet its OD is specified by it's schedule or wall thickness. Tube specifies the outside diameter, e.g. 1/2" Tube has 1/2" OD yet its ID depends on the gauge or wall thickness.
My Turn,
Pipe, as in round iron pipe, schedule thickness pipe, plastic pipe, steel brake line pipe.
Tube, as in square tube, rect. tube, column tube.
Flowline, left to right product line, float glass line, assembly line.
String, flow line of assembly, bob line of squareness, elevation of pipe, ground, platform, concrete, block. Flow line of liquid flow.
Not to be picky but, you're only partially right. ANSI steel pipe is specified by the 'nominal' ID. 2" pipe always has an OD of 2-3/8" regardless of the schedule or wall thickness. This only applies up to 14" after which pipe is specified by the OD. I'm not sure how other materials such as copper or PVC are dimensioned but I would imagine the OD is kept constant to facilitate standard threads and/or couplings.
