what you have available right now, than use it, until you can get another tank, 
The 20 gallon they are talking about is a 20 LONG if you get the chance to look at one, theres a difference between the reg and long.
As far as veggies these guys are bug eaters. I do offer small pieces of greens (collads, kale, dandelion shredded carrot, squash, shredded apple) a few times a week,
I have some that will nibble, and some who never bother, best thing is to try and see if yours is interested. 
Your last question, was about hybernation. With lizards its called Brumation, and yeah, your right most people brumate them if they want them to breed.
But sometime down the line when you get used to everything, you may want to do it, as it's believed to be good for them, like a rest period.
You usually do not brumate the very young, or very thin, or unhealthy lizards. They may not do well
This means, when it begins to get colder out and the days shorter and less light, you simulate that by slowly stopping their food intake, and slowly turning of basking light and finally uvb light until temps are lower and they just natually will go into a sleep. You can brumate for a few months. Some breeders get the temps down into the 50's and 60's Some put them in coolers to acheive these temps.
Me I'm a scardey cat, I dont like putting mine in coolers, I just turn lights off, and leave them in their tank.
For the least amount of time I can,
I like them up (Hahahaha) Also have to make sure they get water atleast once a week while in brumation, so they don't dehydrate.
When and if, you want to brumate you can get a more detailed answer, this is just a brief answer to give you an idea of WHAT it is.
I hope your little girl does great, and we can see her pic soon, I can tell you will be a great collared parent already, 
Take care,
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Eve