This is a nice piece of design. Can I check, with Archery I have +4 to attack? Is there any maths behind +5 to damage, or was that intuitive?
I can add that I've been moving to a similar spot. The Hand Crossbow is light, so should be usable as an off-hand attack. (Maybe it was at some point in development?) That one bonus attack seems fine. I like preserving the distinction between the bow and the crossbow. Like you, I've come to see the bow as the skill weapon, with the crossbow as a decent option for the less well trained.
First off, yes, I'm aware that to get the "x-bows need less training" the benefits (bonuses to attack and damage for non-hand crossbows) should be given out for free. In the end, I felt that made a too-great change from RAW, hence the feat. I can of course give the feat to any NPC I like; this way at least when I forget the bonuses no harm is done (the rules are still followed, that NPC apparently didn't get the feat after all).
The hand crossbow is indeed light. (Personal bugbear: the "light crossbow" isn't light) Problem is the rules for ammunition prevents it from being used in one hand, off-hand or not.
I use "use" in the sense "use freely/at-will/every round", not merely "use in first round, then discard". Furthermore, I detest any combat routine involving the abuse and degradation of object interaction: dropping things to free a hand for some action, then picking that thing up again...
For example, as I see it you can't "use" a hand crossbow in your off-hand while you wield a scimitar in your main hand. (You have no hand free to load it, and the dropping your scimitar, reloading the crossbow, and picking up the scimitar routine is stupid and heinous)
If my design is working as intended, you could use a single hand crossbow just like RAW to fire off lots of bolts gun style, except for the fact the loading keyword isn't nullified by the feat any longer. So the most you could do is fire once with your action and once with your bonus action (note how my version of the feat allows the main weapon and the off-hand hand crossbow to be one and the same weapon, just like in the RAW version). Once you gain Extra Attack, you would want to switch to a scimitar or similar, to be able to attack twice with your main-hand weapon, and then the off-hand bonus action hand crossbow attack (without penalty for being in the melee that you so clearly are in if you're using a scimitar).
The point with this use of the feat is to be able to change two shortswords for one shortsword and one hand crossbow, which is what I believe everyone thought the original Crossbow Expert was about.
My version of the feat thus represents an alternative to Dual Wielder. Instead of getting to switch from two light weapons to two rapiers (or whatever), you get to use one rapier (or whatever) and one hand crossbow. The off-hand attack can be either at the target in front of you, or at range, giving you the flexibility the archetype I pictured you evokes. To me, this is the support the game should have provided.
In both cases, you get to do the same number of attacks. A level 11 fighter does three attacks with her scimitar and then a fourth attack with either a dagger (say) or a hand crossbow.
In the case of dual wielder, you need the Two-weapon Fighting style to get your ability modifier to damage on the off-hand attack. In the case of Crossbow Expert, Two-weapon fighting style gives you nothing, so you can take Archery instead. While this only gives you the +2 to the bonus attack, it does help you to switch to a 100% ranged combination (Longbow perhaps). Dual Wielder instead nets you +1 to damage and +1 to AC (and the "dual draw" ribbon feature).
In no case there is a way to do "two weapon fighting" at range, which the PHB allows*. Keeping PCs focused on melee is important and worthwhile.
*) a character with RAW Crossbow Expert can use one and the same hand crossbow for all of his action attacks as well as his bonus action attack, and indeed this is the only configuration that isn't tripped up by ammunition rules. If this character then takes Sharpshooter, he effectively does two-weapon fighting better than Drizzt, since he can shoot at any range between 5-120 ft AND he effectively gets Two-weapon fighting style despite taking Archery instead
Your initial questions:
Yes, the +2 bonus stacks with Archery. Of course, I have tweaked that fighting style to add "+2 against targets
with cover". But yes, it still makes +4 where applicable.
The +5 is simply the damage bonus a maxxed out ability would give you. The heavy crossbow comes with "Dexterity 20" as it were. And yes, the +5 would stack with any Dex bonus you yourself possess. For untrained rabble, though, it means there is a weapon that can give them a great ability score. I find this makes crossbow troops considerably less obsolete once the PCs are past the first few levels. Now all they need to do is hit...
So as the final note: yes, it's almost as if the feat is two separate feats in one. On one hand it boosts single-attack users that don't mind having to use both hands: a valor bard perhaps, or NPCs, using a light or heavy crossbow.
On the other, it provides an alternative way to get at "dual wielding" where one weapon is the hand crossbow.
