Both a) and b) are slightly wrong:
a) He can make 3 attacks with hand x-bow (2 with [Extra] Attack Action and 1 as a Bonus Action) and 5 when using Action Surge. Action Surge gives an additional Action and using Attack Action gives him 2 extra attacks due Extra Attack rule. (PHB 72)
b) Any ranged attack can be made in melee without disadvantage with the Crossbow Expert feat. This even includes spells. Usually every feature has a more general benefit and this is the one on Crossbow Expert. (PHB 165)
While long bow has +1 greater average damage than hand x-bow the extra hit is well more worth it as you also gain your stat bonus with every hit. With a +3 DEX modifier Longbow does 15 (2d8+6) average damage with 2 hits and hand x-bow does 19.5 (3d6+9) with 3 hits.
IMHO the best advantage that the hand x-bow gives is one more attack roll to not miss with. String of bad rolls is what usually gets someone killed and with hand x-bow you get to roll one more time. With Sharpshooter feat the biggest disadvantage of hand x-bow is negated as you don't have to be within 30 feet to be effective. JP really needs to remember to gather bolts after fights as he will be using tons of them.