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.

The answer is yes.

Crossbow Expert: the third benefit works with a net, since the net is used with its own action. - Jeremy Crawford (https://twitter.com/JeremyECrawford/status/756180214565122048?ref_src=twsrc%5Etfw)

What the Net Rule Means

You can't use other secondary attacks in the same "action" as the net attack. It has nothing to do with "losing" the net. Because:

When you use an action, bonus action, or reaction to attack with a net, you can make only one attack regardless of the number of attacks you can normally make.

Is not limited to just attacks with the net. This is limiting use with secondary attack features like the fighters:

Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn The number of attacks increases to three when you reach 11th level in this class and to four when you reach 20th level in this class.

Which is two attacks with one action. Careful reading of what Jeremy's post indicates you couldn't make a second attack with a sword in the same action/bonus action/reaction the net is thrown, but you could use a different action/bonus action/reaction to do it if you have it available.

The net rule is poorly worded, but from Jeremy's post, it is clear this is what is meant by it.

The Feat

When you use the Attack action and attack with a one-handed weapon, you can use a bonus action to attack with a loaded hand crossbow you are holding.

Allows you to make an attack as a bonus action, not part of the action. So you can use the net on the action, and the cross bow on the bonus action. No net rule violated.