Jormuntide Ignis – Savage Lava Dragon

I have multiple copies of the same card with a [Once Per Turn] ability in my base. Can the [Once Per Turn] ability be activated once for each individual card?

Yes, it can be activated. For example, if you have multiple copies of TD01-008 〈Stone Pit〉 in your base, even if you activate the 【ACT】 ability of 〈Stone Pit〉 A, you can still activate the 【ACT】 ability of 〈Stone Pit〉 B.

The 【ACT】 ability of BP01-001 《Jormuntide Ignis – Savage Lava Dragon》 states [Once Per Turn]. After paying ③ to activate the ability, can I activate the ability again by discarding 2 cards from my hand?

No, it cannot be activated. Regardless of which cost you pay, a [Once Per Turn] ability can only be activated once per turn.