I have two questions regarding the Arabic letter Raa,

Question
Assalaamu Alaykum Wa Rahmatullaahi Wa Barakaatuhu

I have two questions regarding the Arabic letter Raa,

1. Is trilling Raa mandatory in all cases (ex. fathah, dhammah, kasrah, sukoon, shaddah), only during shaddah or not mandatory at all (Many Qaris in my Masjid say not to trill Raa at all)?

2. I have an inability to trill the Raa, I know some who can do it, but some can't, I am one of the ones which can't. Is there a way I can learn it?

Jazaakallaahu Khayran

Answer
Wa alaikum assalaam wa rahmatullahi wa barakatuh,

1. The characteristic of , or repetition of the letter is an intrinsic characteristic which we have to keep in check and not allow to be in excess.    The should only have one repetition, not excessive trilling of more than that.  is present in all cases of  the since it is an intrinsic characteristic. 

2.  If you are using the correct articulation point of the , you should be able to trill it excessively.  It maybe you need to adjust your articulation point.  Allah knows best. 
Please see:
http://www.abouttajweed.com/the-characteristics-of-the-arabic-letters/characteristics-of-the-letters-part-8-characteristics-without-opposit.html
Wa iyyaakum