Clever, but unlikely
In order for Catapult to work, it requires:
one object weighing 1 to 5 pounds within range that isn’t being worn or carried.
This is the requirement that Delayed Blast Fireball must meet. The question is: Does it?
Delayed Blast Fireball isn't explicit in the definition, but it does state:
A beam of yellow light flashes from your pointing finger, then condenses to linger at a chosen point within range as a glowing bead for the duration.
How much does a bead of light weigh?
In order for that bead to qualify for Catapult, it must be at least one pound and less than five pounds. As Dale M states, that's likely a DM call. But how should the DM approach?
Well, it's a beam of light that condenses into a bead. How much does a bead of light weigh? I'd think that a bead of magic light does not weigh anything, but another DM may believe otherwise. Then it's a question of does a bead of light weighs more than 1lb. Even if it did have a mass, it's unlikely to weigh more than 1lb.
Without meeting the weight requirement, you can't use Catapult to launch the Bead for extra damage (pending the save failure).
Throwing the Bead
There is another option for interacting with the Delayed Blast Fireball:
If the glowing bead is touched before the interval has expired, the creature touching it must make a Dexterity saving throw. On a failed save, the spell ends immediately, causing the bead to erupt in flame. On a successful save, the creature can throw the bead up to 40 feet.
This does imply that it can be handled, but it doesn't answer weight or anything else. Ultimately, this is a magic bead made of condensed light and it does not necessarily mean it has mass. It just means that you can throw the magic bead. If a DM does rule that it has mass, then it still needs to weigh more than 1 lb (see discussion above on weight of condensed light.)
Nope.
From the DMG at "Objects" (p.246):
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone....
Your gases and liquids aren't "discrete items" in any natural-language sense of the word, so they're not (game) objects and aren't valid targets for animate objects.
Best Answer
No, you can't use the net to restrain targets this way.
Since the net is a weapon that you use an attack roll to hit with, then you must make an actual attack with it. If the net were an object that you threw, it would be used with the Use an Object action, like siege weapons are described. Sure, the description says "when you hit something" with the net, but you must read it within context.
It's not just throwing a curled up net at a creature; you have to attack with it.
Another thing to pay attention to is the actual spell description.
The impact always causes 3d8 points of bludgeoning damage. If you threw an axe with catapult, you wouldn't deal 1d6+STR as if you had made an attack with it, you would instead deal 3d8 bludeoning from the impact.
Whatever you throw is just a placeholder; there are no special properties for items.
enkryptor also makes a good point. 5e uses the hit terminology for a successful attack roll. In the spell description, the projectile is striking something, not hitting.