In "The Love Song of J. Alfred Prufrock," why will Prufrock wear his trousers rolled and why won't the mermaids sing to him?

Throughout the course of this poem, Prufrock reveals,
through the stream-of-consciousness style of writing, all of his insecurities and fears
about himself and his life.  He cares greatly for a woman, and wants to express his
feelings and ask her something (experts suppose a marriage proposal), but he is worried
that she will reject him and mock him.  He is worried that she does not feel the same
way at all, and that he will make a fool of himself by revealing his feelings when they
won't be returned.  So, in his imaginings, he imagines himself growing old; part of the
imagry involved with growing old is reflected in the phrases "his hair is growing thin,"
and "but how his arms and legs are thin," and other such things that happen to men when
they grow old.  They look and dress a certain way.  The reference to him rolling his
trousers is another allusion to old men; right before that reference, he declares, "I
grow old!  I grow old!"  So, we know that is on his mind.  Old men tend to wear their
trousers rolled up a bit to avoid tripping.  So, he is worried that he is too old and
insignificant, and that she will view him as a crazy old man, and that he will grow old
alone.

The mermaid reference is a connection to women;
mermaids are mythical, beautiful creatures, women, who, in fable, tend to lure men to
the depths of the sea with their beauty, and then the men drown.  So, Prufrock referring
to the mermaids simply shows his attitude towards women:  they are alluring, beautiful,
untouchable, unattainable creatures that leave him in pain, drowning in insecurities. 
They only sing to people they desire, and he feels that he is undesirable, which is why
they won't ever sing to him.

I hope that helped; good
luck!