If you cast a spell for another cost "rather than pay its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs. If the card has any mandatory additional costs, such as that of Draconic Intervention, those must be paid to cast the card.

If the next spell you cast has {X} in its mana cost, you must choose 0 as the value of X if you pay life rather than pay its mana cost.

Marshland Bloodcaster's ability affects the next spell you cast after the ability has resolved. If you cast any spells in response to the ability, those spells are cast as normal.

Even after the ability resolves, you may choose to not pay life rather than pay mana cost of the next spell you cast that turn. However, if you do this, you won't have the opportunity to pay life for any other spells you cast that turn (unless you activate the ability again).