Just take the Two-Fisted Shooter feat and move on.
You can treat the hand crossbow as an off-hand weapon, and you can reload it one-handed as a free action. When you score a critical hit and have a loaded hand crossbow in your off hand, you can make a ranged basic attack with that weapon as a free action. (MP 140)
This will let you reload a hand crossbow with the hand you're holding it in, and eliminate any other silliness.
It's totally possible to juggle weapons like your talking (actually what you probably want to do is juggle the rapier and the hand crossbow in the same hand and keep your off hand free). But really, there's a feat for this, that has an additional cool mechanical benefit. Take that and move on.
One more possible solution if you don't mind spending a minor every other turn or so.
- Start turn with unloaded HCB in off hand, rapier in main.
- drop rapier (free action)
- Load HCB (Free action)
- attack with HCB (standard action)
- Reload HCB (free action)
- Pick up Rapier (minor action)
You now have a loaded HCB, and the rapier is back in hand. If you do this every other turn, you can attack with the HCB and have the rapier available for opportunity attacks or melee situations.
You can attack three times.
Your first ambiguity isn't really ambiguous at all. The distinction between an Attack action and an attack is pretty clear. Heck, both of the quotes in your question make that distinction.
For reference, the Attack action is defined as:
The most common action to take in combat is the Attack
action, whether you are swinging a sword, firing an
arrow from a bow, or brawling with your fists.
With this action, you make one melee or ranged
attack. See the “Making an Attack” section for the rules
that govern attacks.
Certain features, such as the Extra Attack feature
of the fighter, allow you to make more than one attack
with this action.
Just like the quotes in your question, it refers to the Attack action and an attack as two entirely separate things. So "you can use a bonus action to attack" means that you can use a bonus action to make one attack, not to take the Attack action.
Your second ambiguity is ambiguous; it could mean that each attack with a one-handed weapon allows you to use a bonus action to attack or that the Attack action as a whole does. Fortunately, it doesn't really matter, because:
You can take only one bonus action on your turn, so
you must choose which bonus action to use when you
have more than one available.
So even if every attack you make with a one-handed weapon allows you to make an attack as a bonus action, you can still only take one bonus action and make one attack.
To address your comment, we have the preceding text from the definition of bonus actions:
You can take a bonus
action only when a special ability, spell, or other feature
of the game states that you can do something as a bonus
action. You otherwise don’t have a bonus action to take.
You don't have a bonus action that Crossbow Expert allows you to make attacks with. Crossbow Expert gives you a bonus action consisting of a single attack. Even if it gives you that bonus action twice, (or up to 4 times for high level Fighters), you can still only take it once.
Best Answer
Yes, you can do that.
You can do everything exactly as you described. If you start your turn with a Rapier and a loaded Hand Crossbow in hand you can:
You will obviously look very silly doing so. A DM could at their discretion dispense you from having to go through this sequence every turn by allowing you to stow your Rapier away in its scabbard and retrieve it in the same turn for the purpose of re-loading your Hand Crossbow, or simply rule that you get to reload the Hand Crossbow with a Rapier in hand.
A DM wouldn't be breaking much by allowing you to do that given that you always pick your weapon back up at the end of the turn so you're never in a situation where un-handing your Rapier matters, unless you're fighting in an uncommon situation such as a steep incline, a tight rope or the surface of a liquid when using some water walking magic.