(1)I feel, it is because the asuras in oneself will lose their power as each sense is controlled. Am I right?
Yes, you are right. once we control our senses we will gain real freedom from material modes. It is not true that letting the senses loose will satisfy them. Senses are like fire and the sense-pleasure is like ghee. The more you give the more it burns!
(2)Is there any particular order of controlling senses so that it will be easy for one to stop getting desires? For example, controlling mouth first, then tongue, nose, eyes, mind etc.
Not exactly but from practical experience of myself and seeing numerous others, chanting the holy names can easily help us to control our sense. According to the scriptures chanting of Hari's names is the yuga dharma. So first use your speech for taking His names and eat prasadam of Vishnu (offer whatever you cook with satvik ingredients to Him). Then the rest will be easy. If you eat food that ignites your passion and ignorance you will be overcome by lusty desires. One who controls the senses is called gosvami (master of senses). In regard to sense control Srila Rupa Gosvami states in Upadesamrta:
A sober person who can tolerate the urge to speak, the mind’s demands,
the actions of anger and the urges of the tongue, belly and genitals
is qualiﬁed to make disciples all over the world.
The ideal way to control all the senses is to try to use them in the service of Lord Krishna. One of the ideal example given in Srimad Bhagavatam is that of Maharaja Ambarisa.
Maharaja Ambarisha always engaged his mind in meditating upon the
lotus feet of Krishna, his words in describing the glories of the
Lord, his hands in cleansing the Lord's temple, and his ears in
hearing the words spoken by Krishna or about Krishna. He engaged his
eyes in seeing the Deity of Krishna, Krishna's temples and Krishna's
places like Mathura and Vrindavana, he engaged his sense of touch in
touching the bodies of the Lord's devotees, he engaged his sense of
smell in smelling the fragrance of tulasi offered to the Lord, and he
engaged his tongue in tasting the Lord's prasada. He engaged his legs
in walking to the holy places and temples of the Lord, his head in
bowing down before the Lord, and all his desires in serving the Lord,
twenty-four hours a day. Indeed, Maharaja Ambarisha never desired
anything for his own sense gratification. He engaged all his senses in
devotional service, in various engagements related to the Lord. This
is the way to increase attachment for the Lord and be completely free
from all material desires.
(3)Is it also true that one who controls the senses are dearer to the Supreme being?
Yes, Lord Krishna:
Bhagavad Gita 2.61 One who restrains his senses, keeping them under full control, and
ﬁxes his consciousness upon Me, is known as a man of steady
Bhagavad Gita 5.7 One who works in devotion, who is a pure soul, and who controls his
mind and senses is dear to everyone, and everyone is dear to him.
Though always working, such a man is never entangled.