Dihada's Ploy counts the total number of cards discarded, including the card you discard as part of its effect and any cards you discarded prior to its resolution this turn. If you cast it with jump-start, this includes the card you discarded 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.

If the card draws are replaced by another effect, you will still discard a card and gain life. If you don't have any cards to discard, it will still count any cards previously discarded this turn.

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.