Hi Varun,
For your first question, yes featureCounts will count the fragment if your 2nd read does not map to the exon of interest. But please be aware that if your 2nd read maps to a different exon then featureCounts by default will not count the fragment due to multi-overlapping.
For your second question, yes featureCounts will only count it as 1 fragment.
Cheers,
Wei