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The ADS diode model will work for a Schottky contact. To my understanding the diode model will work for any diode which exhibits a non-linear I-V ~ I=Is e^(Vd/nVt). In the ADS schematic you will have to include the diode model parameters and fill in the appropriate values for a Schottky contact: Is, Rs, Cjo, Vj, ...etc.. Data sheets for existing Schottky diodes on the market could give you starting point for these values if you don't have a specific contact area, substrate, and doping level you must use.
Harmonic balance will work for non-linear analysis. You will have to label the node which you want to plot the spectrum of, in your case the node connected to your 50 ohm load.
Your circuit topology isn't quite set up to act as a mixer, I am assuming you wanted to create a frequency down converter. You will need a second source, the LO, to modulate the diode. There are many example topologies on line and within the Agilent/Keysight documentation.
No, this will not simulate correctly. Simulation is wrong if you use the wrong type of circuit models, or in your case ideal wires.
The reason is that this ring resonator needs coupling to the other lines, and model-based simulation includes that coupling only if you use models for coupled microstrip lines (MCLIN in the microstrip lines palette, where the "C" stand for coupled). If you use normal microstrip (MLIN) then each line is simulated independently, with no coupling to other lines. And you have used wires (ideal connections) which is even worse than MLIN because it is an ideal connection (no physical length). Use MLIN for the uncoupled lines and MCLIN for the coupled line, then check your resonator.