yes, Muslim men are commanded to keep their beards, although there are differences concerning the length at which it should be maintained. good question. why do you ask?
no you are mistaken lazaru1. There are plenty of authentic hadiths commanding to grow your beard and trim your mustache such as this one. "Cut the moustaches short and leave the beard (as it is)." - Sahih Bukhari 7;781 & another just so you need more proof "Trim closely the moustache, and grow beard, and thus act against the fire-worshippers" - Saheeh Muslim
there is no command in the hadith or koran for men to grow beards. prophet muhammed grew a beard as was the norm at the time, but removed his moustache to differentiate himself from the other faiths locally
There is no asceticism in Islam. The prophet was NOT an ascetic. He preached moderation and development. It is not up to muslim to give up on the world in any sense. The hadith are so diverse that one can interpret anything and use them to support contrary arguments. The Al Buhari hadith were compiled 400 years after the Prophets death and full of contradictions, Aisha herself has pointed out many hadith as being untrue by her contemporaries. Islam is for education, development and progress.