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.)
RAW, yes.
There is no restriction on the Simulacrum's ability to regain other expendable class feature. Additionally, any creature can take a short or long rest (and thereby restore the expended class features).
For Sorcery Points, you could even make new spell slots
The Simulacrum has this restriction:
The simulacrum lacks the ability to learn or become more powerful, so it never increases its level or other abilities, nor can it regain expended spell slots.
However, the Flexible Casting feature allows you to:
...transform unexpended sorcery points into one spell slot as a bonus action on your turn. The created spell slots vanish at the end of a long rest.
This ability is not restoring expended spell slots, but creating new ones. Therefore, it is allowed.
But Crawford has clarified that the intent is for other resources to be expended permanently as well
In this tweet, Crawford says:
Simulacrum—the spell's creation can't gain levels or regain expended spell slots (RAW). The creation is meant to be unable to regain use of any of its features that it expends (RAI).
This shows that there is a clear distinction between the way the feature is written and how it is meant to be used. It may even be errata'd to reflect this. Ask your GM whether your game will use the RAW interpretation or the RAI.
Best Answer
No.
Trivially, the spell text does not say that a simulacrum knows what its "original" knows. Spells only do what they say they do, so the simulacrum doesn't know what the original knows.
For instance, the Clone spell explicitly states that the soul-infused clone keeps its memories (emphasis added):
Simulacrum does not have this language, so it doesn't retain its memories. It's also worth noting that this text delineates between three key aspects of a character: personality, memories, and abilities. While a simulacrum might know just enough to use its abilities, as detailed by its game statistics, it would not have memories like the location of the cult's secret HQ.
Other support:
It's not specifically stated in the spell, but the wording of the spell suggests that the simulacrum is a different creature that has the same game statistics and appearance as the original.
Below, I've bolded the places in the spell that show how the duplicate is different from the original:
Thus, the simulacrum has the appearance of the original creature, but nothing else.
Moreover, just because two creatures have the same game statistics doesn't mean they have the same knowledge--you can have two wizards that have the same stats but different knowledge, for example.
As for spells, as you point out, the text refers to expended spell slots, which seems to assume that the simulacrum does keep the spellcasting class feature of its original.