Each world has two houses available, a larger estate (you can place 150 items outside and 250 items inside the house) and a smaller one (you can place 50 items outside and 150 items inside the house). The houses get more expensive as you "go up in the worlds".
In WC the small house (the house consists of a loft area (bedroom?) and a somewhat large living space downstairs) costs 8000 gold, and the larger version (the house has three levels with 3 small rooms and 3 large rooms, a large outdoor theater room, and water area) is 15000 gold.
Krok small is 10000 gold (it consists of a couple tents), large is 20000 gold (there is a sphinx, OK size 2 level house (5 rooms?), water hole, and lots of sand).
MB small is 12000 gold (1 large upstairs room, 1 large downstairs room, an additional room outside, and a pond), large is 30000 gold (many roomed house, large glass enclosed outside room with stage, another area that would be nice to put any statues you acquire, but you can't go into the water).
MS small is 15000 gold (1 large upstairs room, 1 medium downstairs room, an additional room outside, lots of green and sunshine, and water areas), large is 40000 gold (no upstairs, 3 large rooms?, 2 small rooms, large outside green and water areas with bridges - if I remember correctly lol).
DS small is 20000 gold (sort of large downstairs, 1 room upstairs, small outside patio at the very top third level, and a water area, it is all hardscape but you can place trees on it - that's what my husband did and it looks very nice), large is 50000 gold (I really don't remember much about this one as it didn't appeal to me much lol).
Forest rooms? Either they were putting trees inside their house, or there is a wallpaper in MS (?) that is trees, also a floor that is leaves. So you can change the existing walls or floors with wallpaper or flooring that you purchase from the shops in the different worlds.
Furniture obtained in different worlds go anywhere. But be aware that some furniture is not tradeable to another character. I believe all statues are not tradeable, and the "free" secret furniture is not tradeable. You can also obtain furniture from quests. To find more info about where to obtain this furniture, look at the Wizards Central Web site (wizard101central.com, under Housing, stickied). And, of course, you can actually buy some furniture.
Also, on the same website mentioned above, some people have made videos of their houses so you can preview some of the houses there.
Hope that helps some. Happy Wizarding!