Need a little guidance / new Boa

[bcr229]

Craigslist ad "female emperator boa" , Location is like 1 street down from me, I can walk there in minutes.

I figure "emperator" should have been "Imperator" so it would be a BCI?

Yes

Was told owner had it since little and it was 2 years old and female. She measures about 3' and weighed in at 562g when I got her home.

Being female it's going to get 7+ feet full grown in 3 or so years?

I would expect she'll get to 5-6 feet over the next three years if fed conservatively, and after that she could end up at 6+ feet.

I was also told she hadn't eaten in 3 weeks and would need fed, she was fed bi-weekly (this is correct feeding schedule?) and had a shed in there in which she refused food that week too.
I had a 75g small rat that I attempted to feed her Sunday night and she took it no issues. So it that size appropriate for a bi-weekly feeding?

At her size/age you could give her a medium rat every three weeks.

I currently have her in a 20L tank, 90* hot side (using a che), thermostat will be delivered today and she will have a uth running then, and 78* cold side, 52% humidity is this correct? or does it need to change?

I would move her to the 36"x18"x18" Exo-terra you mentioned as it should last her for at least a year. Temps and humidity sound fine.

She was in the cage pictured, I was given it too, I see no way to control temp or humidity. But was going to clean it up good and use it for a "play area" for the boa and my Corn snake to give them a place to explore and climb. Good idea or no?

I like that idea. It's also good to have somewhere to safely stash a snake temporarily if you need to do deep-cleaning or maintenance on its regular enclosure.