Found an Iguana

[The Bearded Derek]

I just found a green iguana in my neighbors house just sitting on their floor in the backyard. They thought it was dead and they asked me to pick it up because they were scared lol. So it turns out it was alive and had a tiny hole by its back leg (probably by their cat) and I put it in a 30 gallon tank that I had just sitting there (I know it's probably way too small, but it's what I have at the moment, doubt I might even keep it)

Just wanted to ask a few basic questions.
I know they're herbivorous but specifically what do they prefer to eat and some foods I should avoid?
Should I have the tank in the sun? ( I don't have a spare heat lamp) I think she (looks like a female to me from the lack of pores) should be fine as long as she has a hide
Should I give her some sticks? Only trees I have are an avocado tree and my neighbors mango tree. Not sure if the avocado's leaves are also toxic. She is wild and who knows how long she's been living in the area, I'm fairly certain that mango leaves at least aren't toxic.
She's also about 6 inches long from snout to vent, 20.5 if you include her tail.
Doesn't seem to be doing good, she's pretty lethargic, probably due to the cold, she does try to move a bit choppy and somewhat weak when I grab her, but she stops after a few seconds (doesn't have signs of MBD though). She feels a little dry too. Food wise, she doesn't seem to be eating but she's not super skinny. I also applied some rubbing alcohol (tiny little drop on top of a napkin) to her wound, didn't seem to hurt her, she didn't budge when I did it.

[The Bearded Derek]

Welp, never mind now, it appears it died. Took her out an hour ago and she was moving the same as yesterday, but she wasn't breathing and her eyes weren't closing. She also had a tiny black thing on the front of her lip, turns out it was the tip of her tongue that she accidentally bit or something. It also pooped during the night and the urate was a bit yellow (not a really bright yellow) so looks like it was dehydrated too. I also put her upside down for a few seconds to see if she'd at least attempt to turn back up, which she didn't even budge.