Does anybody know good exercises to learn to pronounce /ы/, /ч/, /щ/ and palatalized consonants?
Have you ever tried Forvo services? This is a big database of pronounced words and expressions in various languages including Russian, so listening to the samples there could be very useful for your students. It could give them an idea how to pronounce some typical syllables and palatalized consonants. Also, there you may place a request on pronunciation of particular words.
Russian pronunciation guide - Forvo: http://www.forvo.com/languages/ru/
It is not suitable for everyone, but an analytical mind will find valuable information in
Quite theoretical, though. Allows to have a deep understanding.
For auditive memory, you obviously need something else, this is more something for people working with visual memory.
I have no idea how to teach to pronounce Ы, but I have a success story on teaching correct Щ.
One man I've taught was French, and for him pronouncing Щ was a literally a nightmare. After several attempts that finally failed, we've tried following trick:
Pronounce Sh for a while, try to make it as lengthy as possible. Now try to whisper and hiss like a snake. Now, while doing all these, slightly move forward (towards upper teeth) the tip of your tongue. Automatically, the middle of the tongue will raise up towards the palate.
It turns out that this is Щ :)
The second my "student" has been an Australian. We've did the same trick with him. It was far easier, since, as we've both noticed, he pronounced
she very close to
As for Ч, I've never met someone who had not been able to pronounce this clearly enough )))