Rulings

The token copies exactly what is printed on the creature and nothing else (unless that creature is copying something else or is a token; see below). It doesn't copy whether that creature is tapped or untapped, whether it has any counters on it or Auras and/or Equipment attached to it, or any non-copy effects that changed its power, toughness, types, color, and so on.
If the copied creature has {X} in its mana cost, X is 0.
If the copied creature is copying something else, the token enters the battlefield as whatever that creature is copying.
If the copied creature is itself a token, the token created by Quasiduplicate copies the original characteristics of that token as stated by the effect that created it.
Any enters-the-battlefield abilities of the copied creature will trigger when the token enters the battlefield. Any "As [this creature] enters the battlefield" or "[This creature] enters the battlefield with" abilities of the copied creature will also work.
You must still follow any timing restrictions and permissions when casting a spell with jump-start, including those based on the card's type. For instance, you can cast a sorcery using jump-start only when you could normally cast a sorcery.
A spell cast using jump-start will always be exiled afterward, whether it resolves, it's countered, or it leaves the stack in some other way.
If an effect allows you to pay an alternative cost rather than a spell's mana cost, you may pay that alternative cost when you jump-start a spell. You'll still discard a card as an additional cost to cast it.
If a card with jump-start is put into your graveyard during your turn, you'll be able to cast it right away if it's legal to do so, before an opponent can take any actions.