Just note that the correct form is "מִכְֿחוֹל" = Mihkhol (rafe).
Most people say Mik'khol, though
why is it written like blue
Because originally מִכְחוֹל was a brush used to apply blue eyeshadow.
Ha'mik'chol¹ ha'kachol shavur.
¹ On pealim.com as michchol. On Wiktionary.org as michekol. But other sites (including teachmehebrew.com) have it as I wrote it.
I do not hear ר in the audio.
Yes, it is pronounced very weaky (as this kind of uvular /r/ is part of my native tongue, I have a good ear for it, and even I must strain my ears to hear it here).