By intently contemplating on the beauty and qualities of his beloved, his sadness dissipated.
By chanting Lord’s names, the ultimate attainment is had.
By seeing this mountain, His memory of Govardhana hill was aroused.
By remembering him, it is seen that he is endowed with all the good qualitites.
By remembering his beauty, the minds of everyone are eternally attracted to him.
By reciting these names, all obstacles are vanquished.
Yes, there are problems of dangling modifiers. We could call that dangling gerund as the v+ing terms in these examples are gerunds rather than participles; they are objects of the proposition by.
Another example of a dangling gerund problem is shown below, and more details can be found here
After roasting for three hours, we turned the oven off.
In this sentence, the modifier after roasting for three hours is positioned next to we, meaning that "we" have been "roasting for three hours."
Possible ways to rephrase the examples are shown below:
By intently contemplating on the beauty and qualities of his beloved, he eased/dissipated his sadness.
By chanting Lord’s names, one achieves the ultimate attainment.
By seeing this mountain, he aroused his memory of Govardhana hill.
By remembering him, one sees that he is endowed with all the good qualitites.
By remembering his beauty, everyone has his/her mind eternally attracted to him.
By reciting these names, one vanquishes all obstacles.