Hi Almagra- I can honestly dismiss your first question, and will halfway answer the next two. It's not that they're confusing, just that I'm not knowledgeable enough to give good answers.
1. There's no reason to worry about verbal categories, like "material substance". Nature doesn't care what names we call it. The real substance of this question is contained in your next two.
2. When we say that gravity isn't a force, we mean that if nothing but gravity is present, the paths through spacetime followed by any objects depend only on their prior paths, not on any properties whatsoever of the object- not charge, not mass, not anything. Thus gravity can be viewed as a geometrical property of spacetime, not as a particular force between objects. General Relativity develops this view mathematically, and for strong gravity, or objects moving near the speed of light, it leads to different predictions than one would obtain for a force in the spacetime of Euclid-Newton. Because the geometry is not
the Euclid-Newton geometry, straight lines ("geodesics") can intersect more than once. That's just like geodesics on a sphere. If you and a friend start at the South Pole and head absolutely straight in different directions (as much as the geometry allows) you will get farther apart, then closer together, and then bump into each other at the North Pole. You could invent a 'force' that pulled you together, if you didn't know that the earth surface was not one of Euclid's planes.
If your geodesic intersects the Earth’s twice, you might say you jumped up and fell down. You could describe that pretty well by pretending you lived in a Euclid-Newton spacetime and saying the Earth’s gravity exerted a force on you, causing you to accelerate.
3. I don’t believe that the categories ’space’ and ’time’ are distinct enough to allow you to say that only one or the other is curved, at least in some way that would be agreed upon by any legitimate reference frame. However, using a conventional frame and describing objects that move slowly in it, it is the curvature of time that accounts for ordinary gravitational forces. Things higher up have more energy which corresponds to higher frequencies. General Relativity says that the clocks at the top of a building then must run faster than the ones at the bottom, and that effect has been confirmed.
As I said, the answer is a bit shoddy, but perhaps it will get you started on a path toward the actual mathematical theory.
Ordinary gravity is well approximated by forces in flat space, i.e. by potential energies which depend on position. It turns out that for objects moving at or near c (in your frame) such ’curved time’ effects account for only half the gravitational curvature of their paths through space. The rest requires curved space.
(published on 10/22/2007)