Is the computer always right?

Given enough time to calculate, in the vast majority of positions, it will be right.

Engines still have some positions that don't evaluate correctly, where stepping into the next move completely changes the evaluations.

Now, what's best for a computer may not necessarily be the best for humans. Computers don't have the same weaknesses humans do

Always looking for or expecting the "best move" is unrealistic and counter productive to your improvement. You're playing low rated players not engines.

I think evaluations by strong engines are about 99% accurate. CPUs aren't infallible.

The engine assumes your opponent will play every best move, see everything, and have 100% accuracy. This is why sometimes the engine's explanation for a move delves deeper into chess than any human could compute.

Very rarely, yes.

Take this famous position, for example:

Stockfish rightly says Black is better here, but it usually (though not always) fails to see ...Bh3!! until you either put the engine on its highest setting or actually play it.

Plaskett's Puzzle is another example; the engine typically doesn't realize White is winning until the move Bc2+!! is played.

The engine is just a tool. You shouldn't blindly trust that it will give you the best results and shouldn't automatically think that its analysis is garbage. Instead of questioning the accuracy of the engine, spend some time learning how to gain the maximum benefit from using it.

What I can't understand is this. Why in analysis at a 40+ depth the engine tells me "this" is the best move, but when I put it on the board, it goes on telling me it is "excellent", but not "best"?

yes

No. I turned my computer left moments ago. Now it's left.

No, I am always right.

What do you have configured as your local engine?