1) My reads are 36nt long. How much should I set for "the Minimum length of reads segments" to get the most reliable output with the highest mapping of splicing junctions?. In my previous run of TopHat, I set it as 18. Can I reduce it more to get better mapping on splicing junctions?

You'll need to define for yourself what you mean by "better/best mapping" and experiment to find the parameters that give you the best results.

2) I do not understand exactly how TopHat works as for the "Anchor length" although I have read the manual for TopHat.
Suppose I set the "Anchor length as 8 and the "Maximum number of mismatch that can appear in the anchor region of spliced alignment" as 0 when I run Tophat. Does it mean, for a read maps on two adjacent exons, TopHat will report this alignment to the outputs ".accepted hits" and ".splicing junctions" if either end of the read has 8 or more nucleotides mapping on one exon?

I think that's correct.

3) Is there disadvantage/negative effect if I choose to set the "Anchor length" at the lowest, for example 3? My understanding is that, under the 0 mismatch condition, if 3 nuceoides of one end of a read mapped on one exon, the other part of the read will map on the adjacent exon (in my case, the other part would be 33 nucleotides). So my understanding is that setting the "Anchor length" at 3 does not increase the inaccuracy of the alignment. Am I correct?

Setting the anchor length especially small reduces the constraints on mapping, so more reads will map but there are likely to be more false positives as well.

Good luck,