So, does the 2nd trait give her an extra close attack in addition to the Colossal Stamina?

Yes, the FREE gives an attack in addition to the other effects.

You're Only Going To Make Her Angry!: FREE: If Giganta has 2 action tokens, "Colossal Symbol" until your next turn and she may make a close attack. After resolutions, deal her 1 unavoidable damage.
If she makes the FREE close attack, will she still be dealt the unavoidable damage?

It's actually a bit worse (damage-wise) than you envision. If you activate it, you get the extra attack, and then she will get injured. If she can already make a non-free action (maybe she was pushed last turn, or carried by someone that allows it), then she will have Colossal Stamina and can continue to "push" that way. She'll still take the extra damage for that.
Effectively, this means that once she has two tokens, she could be taking 2 damage a turn, but making 2 attacks per turn, as well. It's not quite worth the tradeoff, but you do at least get to make regular actions (such as EW and CE) with that Colossal Stamina. I'd just rather have Flurry. Of course, if Flurry is that non-free action you take, she can end up doing 3 attacks. That can be a little scary.

Sweet mercy...so, let's say she used her indomitable to either move adjacent to an opposing character or to make an attack...now she gains the 2nd action token...she can then right then and there make her free attack and take the damage...then...on my next turn, while she still has the 2 action tokens, make the free attack again, take 2 damage because of the colossal stamina and the trait?
If so, I'll take it!!! With extra mayonnaise please...

Awesomesauce. Bring along a medic, and she's hitting hard every turn.

Hm... get a couple medics, a Proteus, and some alternative mode of transportation, could this thing get super-stompy?

Force Build 8951651 0
Set	#	Name	Team	Pts	Value
HQ	055	Giganta		90	SELL
UXM	057P	Proteus		35	SELL
YGO	044	Mystical Elf		50	$14.63
BVS	010	Alfred Pennyworth		30	SELL
AAOU	010	Scarlet Witch		55	$1.94
JW	050	The Penguin		40	SELL
Force Total:				300	$16.57

A couple of healers (push Alfred hard), a Scarlet Witch to provide full +1s, and a Penguin to keep character count at 6 (unless bystanders don't count as characters, I forget how that works, in which case it's easy to find point-filler). This particular lineup would be kinda rough to actually play, but it's a concept.

Haha, she looks like she's wearing the same big fuzzy slippers that my girlfriend owns.

Can't equip Proteus to Giganta

Right... Forgot about that size restriction.

All this for the bargain basement cost of 90 points.

Ridonkulously min-maxable, so it's a good thing she has that trained Stealth; she's got a big target on her head as soon as she shows up. Hard to argue she's not the best Giganta we've seen yet, and essential for Secret Six teams; still, I may keep the old FF SLOSH version for the classic outfit and end-dial Outwit.

Being able to make 5 attacks in 3 turns? No way I am playing her without Red Leader and Jane Foster.

3rd turn, free attack, drop to click 2, colossal stamina flurry for a possible 13 damage (if she has 5 teammates)in one turn. She's going down, but she's taking more than her fair share of opponents with her.