@hum

A "hum", also called /anusvAra sound, is made by closing your lips and humming.

The anusvAra letter (M ं) is always to be pronounced as a hum sound whenever it is before h ह् y य् r र् v व् l ल् z श् S ष् s स्. This letter is not pronounced as a hum sound elsewhere.

The hum sound does not appear elsewhere in modern spoken Sanskrit. But sometimes you can hear it elsewhere in Vedic recitation.

/pANini disagrees with what you say. According to /pANini I may pronounce the "Mp" in "taMpazyati" either as "tampazyati" or as "ta" + hum + "pazyati". Why do you say that I can't hum?

You may hum there, according to /pANini. It's just that those hums are rarely heard nowadays, so I always strongly advise my students to only hum before h ह् y य् r र् v व् l ल् z श् S ष् s स्.

I read somewhere that the /anusvAra is not a letter, but a diacritic sign that shows nasalization of the previous vowel, like in French "bon".

That's the sort of BS that people making books copy from earlier books.

It is true that the /anusvAra letter sometimes shows nasalization of the previous vowel, but that happens in Hindi and other Indian languages, never in Sanskrit. When you want to show that a vowel is nasalized, you add a /candrabindu atop it, not an /anusvAra letter. See sUtra U~ for an example.

Yet, I have a Sanskrit grammar book where sUtra U~ is spelled as UM ऊं.

I call that a misspelling. When the font you are using has no /candrabindu type available, you use the M ं type instead. Where's the /candrabindu key in your keyboard?