I am wondering if these "non-coding reads" will be included when cufflinks calculates transcript/gene expression.

Reads will only be included if they map to assembled/known transcripts.

And another question is:  how to know the number of reads mapped to a certain exon?

This isn't possible because a single read may map to multiple exons and/or transcripts. Cufflinks assigns reads probabilistically when their mapping cannot be uniquely determined.

See

http://cufflinks.cbcb.umd.edu/faq.html#count
http://cufflinks.cbcb.umd.edu/howitworks.html

for details.

Best,
J.