"Is it very difficult to get the persmission for a marriage between non-Qatari woman and Qatari man?"

It depends who you are? where you come from? Basically your full background.

You will not be obligated to convert.. God says: “Let there be no compulsion in religion” [Surah al-Baqarah: 256] and you can easily win the family of this Qatari man by being respectful and uderstanding to his culture and religion.

Wearing the abaya or your lifestyle in general,having children,your career..or whatever life issues i guess this should be discussed prior to getting married whether your guy is Qatari or not.

"I would like also to know the opinion of Qatari nationals regarding this topic and that of foreigners married to Qataris."

Yeh...YOU NEED TO STEP OFF OUR MEN!!!