Improve documentation

This issue is to collect feedback that I got from students regarding the documentation.
I will continue this issue in the future with more feedback from more students/users.

• using Pkg; Pkg.add("OrdinaryDiffEq", "Plots") doesn't work.
• Add images of shapes to the docs (rectangle, sphere, etc.).
• Add docs on how to visualize initial conditions for easier simulation setups.
• Continue the method theory page and make it easier for users to find out which methods and corrections, density diffusion, boundary conditions are best for which use case.
• Add more "developing TrixiParticles" information like best practices and conventions (format, comments, etc.).
• Make clear that API reference is inside the components docs (#660).
• Clarify update steps. Why is compute_pressure separate from compute_quantities?
• Mention in the docs that test_util.jl has to be included before running an individual test file.
• Mention that density of fluids is stored either in v or in cache.density.

Treat the checklist as several separate documentation tasks rather than one small change. Start by reviewing the components docs, method theory page, update-step explanation, and guidance around including test_util.jl before individual tests. Done means the selected feedback is incorporated, including the requested examples, explanations, and density-location note.