If i normal summon a monster and Swift Gaia the Fierce Knight then becomes the only card in my hand, am i allowed to normal summon him?

i'm guessing no

It's a basic rule in Yu-Gi-Oh!

You are only allowed to Normal Summon or Set once during your turn unless you have Ultimate Offering in play.

Swift Gaia the Fierce Knight, being a Normal Summon, falls under the same restrictions...it is not a "special" Special Summon.

The same would go for Fusilier Dragon, the Dual-Mode Beast.

Any card that says you can Normal Summon it without Tributes is STILL a Normal Summon in terms of game mechanics.

Swift Gaia the Fierce Knight
Fusilier Dragon, The Dual-Mode Beast
Lightning Gear - Sakuraka (EOJ)

...all take up the Normal Summon slot for the turn unless you got a card like Ultimate Offering that would let you do otherwise.