Without strips (called "stickers") separating the layers of wood, it will not dry in your lifetime - it will rot first. The wood *must* have air circulation on *all* sides in order to dry. And the stickers need to be thicker than 1/4" for proper air circulation: 3/4" is better.
You *must* sticker the wood if you expect it dry properly. This is not optional. You'll have a pile of useless, rotted wood within a year if you don't.
The rule of thumb for air-dryed wood is one year per inch of thickness, plus one year - so figure 5 years for 4" thick lumber, 3 years for 2" thickness. If you live in an area with very low humidity (such as Arizona), it won't take that long; OTOH, if you're in Florida, it could be much longer.
Not enough information to tell. Depends on the species, on the individual tree, what part of the tree the wood came from (trunk or branch), on how the wood was sawn from the log, and on how it's stacked.
If the tree was pretty close to straight when it was alive, the wood came from the trunk and was cut properly and stickered promptly, stacked on a level surface, you won't see too much warping. OTOH, if the tree was leaning, or if you cut lumber out of large branches, it'll warp. (Google search on "reaction wood" to learn why.) Some species (e.g. beech) are prone to warping, others (e.g. black walnut) generally are not. Quartersawn lumber is more stable than flatsawn lumber. And on and on.
For more information:
1) look for a copy of "Fine Woodworking on Wood and How to Dry It" at your local library
2) check out the chapter on drying wood in "Wood Handbook: Wood as an Engineering Material" available on-line at
http://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr113/fplgtr113.htm
3) post your question over at rec.woodworking - several guys there air-dry their own wood, and can give you a lot of useful tips.