1) Generally the two models of QC are the digital/circuit model (analogous to digital logic gates, with some caveats, such as reversibility of operations, no-cloning theorem), and analog computation (tuning the parameters of a continuous-time quantum system in your lab such that the system produces useful output)

2) The physics/architecture/organization depends heavily on the type of computer being discussed. In classical computing, one "type" of computer has won the arms race. This is not yet the case for quantum computers, there are several different physical processes through which people are trying to generate computation, trapped ions, superconducting qubits, photonics, quantum dots, neutral atoms, etc.

3) There are several ways that you can simulate quantum computation on classical hardware, perhaps the most common would be through something like IBM's Qiskit, where you can keep track of the degrees of freedom of the quantum computer throughout the computation, and apply quantum logic gates in circuits. Another, more complicated method, would be something like tensor network simulations, which are efficient classical simulators of a restricted subset of quantum states.

4) In terms of research, one particularly interesting (although I'm biased by working in the field) application is quantum algorithms for nuclear/high energy physics. Classical methods (Lattice QCD) suffer from extreme computational drawbacks (factorial scaling in the number of quarks, NP-Hard Monte Carlo sign problems), and one potential way around this is using quantum computers to simulate nuclear systems instead of classical computers ("The best model of a cat is another cat, the best model of a quantum system is another quantum system")

If you're interested in learning more about QC, I would highly recommend looking at Nielsen and Chuang's "Quantum Computation and Quantum Information", it's essentially the standard primer on the world of quantum computation.