Am i correctly understand that following string means Nimble I gives player +20% to total speed (including other speed bonuses) and Nimble III gives +60%?
If not, can you tell me please how it exactly works?

AttributeModifier speedModifier = new AttributeModifier(nimbleUUID, "Nimble", (float) enchantmentLevel * 0.20000000298023224, AttributeModifier.Operation.MULTIPLY_TOTAL);

Yes what you are saying is current.