Every walkthrough for Strahd's possession seems to suggest that we should have an elf and a dwarf in the party to spot hidden buttons and walls. Is this really true? Do half-elves suffice instead of elves? How much of a hassle is it to play without this? Can companions fill this role?

I feel this severly limits character options if we're can't use most of the races during character creation...

It's mostly a quality of life thing I guess. You can still spot these buttons yourself. I didn't have any problems without a dwarf/elf; thanks to automapping it's often easy to see where a secret room might be, and a button is often close by.
For secret walls: Same deal, if the map shows there could be a room somewhere, just run into the walls surrounding this empty spot.

SSI's dungeon crawler map layouts and puzzles are rather easy when compared to, for example, Westwood's games.

Yeah, it's not really necessary, just makes for a smoother more fun gameplay experience. If you miss an illusionary wall, that is not game breaking. You just miss out on a few goodies. Not finding a button on a wall may be a plot stopper, though, and then you'll have to resort to pixel hunting.