I have a house with a small yard and very fertile soil. I've decided to buy half a dozen saplings from a local nursery and plant them in the yard so the will the trunk faster. I've come across one interesting method on the Internet, where you place a tile in the ground and plant a tree over it to encourage horizontal growth of the roots and get a nice nebari. Has anyone on the forum tried this method? Could someone describe it in more detail and share their experience?

I do it with every tree in the ground like that, not much to explain, it really is simple as that.
Every 2 years you lift it from the ground and cut around the roots so they don´t go too far.
And back on the tile buried in the ground untill the trunk is thick as required.

I have not yet decided which trees to buy, could you suggest some fast-growing species other than ficus?

Depends on the climate.
I only "field grow" trees that are hard to get or very expensive here, as japanese maples and junipers.
I also have few pines in the ground that I collected but decided I want to get their trunks thicker.
Those species grow quite well in here, I water and fertilize them heavily.

Well I live in the Republic of Georgia. Summers in here are quite warm, average temperature in winter ranges between 2°C - 4°C. I was thinking about pines and really wanted to get a red maple. I think I will have no problem with pines, but I'm not entirely sure about the red maple, if by some miracle temperatures will drop
well below zero, will it survive?

We get -20°C and they don´t mind while in the ground.
Some twigs may die, but while growing for trunk size it doesn´t matter.