Is there a way to quickly verify the presence of some SNPs in Fastq files? Is there a tool that can scan fastq files without assembling them for a custom list of user defined snps?
Try this pipeline: 


Clean raw fastq files (trimmomatic)
Align clean fastq files to the reference genome (dna-to-dna aligner of your choice)
Convert the alignment sam file to bam (samtools)
Call SNPs from bam file (samtools)


Here's a start tutorial on this: http://ged.msu.edu/angus/tutorials-2013/snp_tutorial.html