Hi Komal,
--quantMode GeneCounts should produce exactly the same counts as htseq-count with 3 columns corresponding to the 3 --stranded options in htseq (all other options default, in particular --mode=union).
You do not need to use fixmate in STAR output. With default parameters, STAR will only output paired alignments, so no need for that filtering either.
Uniquely mapped reads are recognized by htseq, so you can simply use htseq-count Aligned.out.sam $GTF > sample.counts
Cheers
Alex