The Crossbow is indeed a VERY strong weapon. Easy to fire, load, and dealing an amazing damage output for such a simple weapon... Technically it makes a bit less sense for them to be a national unit, though with how strong they are right now it's far from unfair.
Easy to fire yes, easy to load maybe, slow to load Very much so. In engagements of bows versus crossbows, the crossbows tend to lose as they can't fire fast enough. Crossbows were more popular because they needed very little training to use competently.
As to Muskets - they are most definitely not the first weapon delveloped after gunpowder was put to military use. The first uses included rockets, firelances, even bombs were a later invention.
Fire lances were basically a container of gunpowder that would ignite on impact, put on the end of a cavalry lance. Its effectiveness no doubt came from watching someone being incinerated. A possible UU for the Dwarven Knight perhaps?
After that very, very basic cannons were developed, all bang sometimes on your own troops and very little buck. the effect was mostly psychological, although they did work. Once decent casting was developed semi effective cannons, seige only were developed. Then slightly usable field pieces. About the same time Handguns were developed - think cannon on a stick, then arquebus -> matchlock -> musket.
Contrary to the common belief muskets were not primitive, they were highly advanced weapons for their time. In FFH going from gunpowder -> musket is very similar to going from archery -> Arbalest (arguably the most advanced crossbow weapon developed)
Gunpowder weapons did not just appear they took almost 600 years of constant refinement to get to what was being used by the Napoleonic era.
If FFH is going to use them then I suggest reworking the current system to get them to fit in better.
Bring Gunpowder in earlier (bronze working), allow it a +

for happiness (fireworks).
Then later allow Handguns and seige cannon (which followed on from the Trebuchet) say Feudalism, the hand gun is a promotion that gives a modest bonus to Melee units (say +10% vs all -25% versus fire - see below)
At Engineering gunpowder gives a +1 to mines?
The appearence of Cannon that work is heralded quite well by Navigation with frigates et al possibly allow actual cannon.
Finally allow muskets in late on, and I agree a national limit, perhaps allow upgrading Royal guard to Musketeers (they were the kings after all!) or call them Dragoons (mounted muskets sort of)
The use of gunpowder won't just appear at the end of the tech tree, which it didn't. Fire based units should do either do extra damage to gunpowder based unit or it should be less effective.
IIRC, China/Asia had gunpowder in the early 1200's. Just some slight real world perspective. I also might be wrong on that.
Crude Cannons first appears in the 1200's Gunpowder was known about for much longer, here there is much more debate. estimates go from decades to hundreds of years.