You are explaining soft consonants very well, I liked it very much! But there's room to improve your own pronunciation! Р in рядом, С in сильный and Щ in возвращался are not enough soft! They sound more like радом, сыльный, возврашался to me.
At the same time, Л' in звали, Х' in хитроумный, Н' in Несарт, Ч' in харчевня, Т' in тепло don't have this bug.

Your дождь is perfect!

Ы also good, but the explanation was too difficult to me (may be because I am not "целевая аудитория"? ) .
Would not it be enough to hint people to go from И as in Beet through иы as in Bit and futher to Ы (I am noticing now, that all I have to do is немного подтягивать язык как бы сокращая его) ?

А Ходжа Насреддин — Википедия кстати - весьма известная в СССР/России личность.