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I also have another question on this model. I found that a direct solver such as "PARDISO" solves the simulation in a considerably shorter time with respect to an iterative solver ( which shows very slow convergence ). Mesh size should be fine enough to capture the physics of the problem. Could the problem be ill-conditioned in some way?

1. You are treating your list of initial pre-defined parametric expressions as if they are functions that will automatically update their values dynamically if or whenever you happen to change one parameter, during the middle of program execution. They don't behave that way. If you want something that will depend on the parameter you call "k," then define and use a function instead, passing it that parameter properly.
2. Pardiso is a parallel direct solver. It is often faster (and more stable) than an iterative solver in RF problems, but it uses more memory than the iterative solvers.
3. FYI, TE20, 30, and 40 are not necessarily the next lowest order modes after TE10 in a rectangular guide. You might want to read more about "rectangular waveguide modes" on the internet or in a textbook. I recommend that you get to know/understand all about TEmn and TMmn modes of potential interest, so you will know what to consider and what to ignore. Good luck.

i did exactly what is explained here https://www.comsol.com/blogs/how-to-automate-meshing-in-frequency-bands-for-acoustic-simulations/ , where parameters are defined as dependent on the parameter which one wants to sweep (no use of functions)

i did exactly what is explained here https://www.comsol.com/blogs/how-to-automate-meshing-in-frequency-bands-for-acoustic-simulations/ , where parameters are defined as dependent on the parameter which one wants to sweep (no use of functions)

Hmm! Well, I'm surprised at that. Nevermind my advice in #1, then. In regard to what is going wrong with your model, I suppose I would take a closer/detailed look comparing what that other model did with what you did. Apparently it didn't connect the parameters/variables in the same way. Might take a while to debug. But perhaps one of the other folks here can find it quickly, especially if they've seen this particular error before. Sorry I couldn't help on that.