Is there an application that can count the number of overlaps between a BED/GTF file and splice mapped pair-end reads?
(e.g. interval 1 in bed is overlapped by 10 fragments)
Yes, BEDTools among others. You can use intersectBed and give it a BAM file with alignments (which can be spliced and paired-end) and a BED/GTF file with intervals.
Check out also the htseq-count tool shipped with the HTSeq Python package.