Europe to USA: How come a detour within Star Alliance cuts the price in half? [duplicate]

Your question, if I may say so, is based on some mistaken assumptions.

First, Star Alliance is not a price fixing cartel. It exists merely for marketing purposes, and provides a bare minimum of integration between the airlines. Turkish Airlines (TK) and the Lufthansa group (LH) are direct competitors with each other, and moreover they are not on "good terms" with each other at all. In particular LH is concerned that TK is taking a lot of traffic away from LH by aggressively undercutting its fares. You will see how they have restructured their frequent flier programme recently to discourage Miles and More fliers from using TK metal.

There is no reason to believe the fares should be the same. Indeed, this kind of price fixing is unlawful in most jurisdictions. The exception, which I can see might cause confusion, is that of course there already is a "Star Alliance" metal-neutral joint venture arrangement between LH & subsidiaries, UA and AC, where the prices are the same between the parties. But TK is not a member of that venture.

The second question ("why is it cheaper to take an indirect flight?") is a simple matter of supply and demand. Demand is higher for direct flights, ergo they are more expensive. I will not re-iterate the point here, except you seem to answer the question "why is it more expensive?" yourself: because you want to take a direct flight when the option is offered to you.

Third, if you drop the legs, your contract of carriage spells out exactly what happens: your remaining flight reservations are cancelled without refund.