Yes, to all of those effects
The first one, preventing a deadly fall, is usually done by targeting an object on your character and using the Sustained Force effect of Telekinesis:
Sustained Force: A sustained force moves an object weighing no more than 25 pounds per caster level (maximum 375 pounds at 15th level) up to 20 feet per round. A creature can negate the effect on an object it possesses with a successful Will save or with spell resistance. This version of the spell can last 1 round per caster level, but it ends if you cease concentration. The weight can be moved vertically, horizontally, or in both directions. An object cannot be moved beyond your range. The spell ends if the object is forced beyond the range. If you cease concentration for any reason, the object falls or stops.
Any worn or carried object is usually a valid target for spells, with saves when the wearer doesn't like whatever is about to happen with their gear. But this is commonly used by targeting your armor, or your backpack, or similar, and sustaining it through the air. You are still targeting an object, but since that object is firmly bound to your character, you also save yourself and is usually accepted by most GMs as a valid use of the spell.
The spell can be cast on objects, which receive saving throws only if they are magical or if they are attended (held, worn, grasped, or the like) by a creature resisting the spell, in which case the object uses the creature’s saving throw bonus unless its own bonus is greater. This notation does not mean that a spell can be cast only on objects. Some spells of this sort can be cast on creatures or objects. A magic item’s saving throw bonuses are each equal to 2 + 1/2 the item’s caster level.
While there are no rules as written stating what distance you fall per round, it is commonly accepted, even by one of the game designers, James Jacobs, that the 3.5's FAQ about falling distances is a valid source to calculate that. Namely, a creature (or object) falls 576 feet (or 500 feet to keep it simple) in the first round of a fall, and 1000 feet every round after that. As such, any fall greater than 500 feet should allow the character one turn to react with at least a Standard Action such as casting the spell.
There is only a brief mention of this in the rules, under Enviromental Rules: Falling:
A character cannot cast a spell while falling, unless the fall is greater than 500 feet or the spell is an immediate action, such as feather fall.
On the second, levitating yourself, again, applying that same logic, you could levitate either a piece of equipment, a rope that you are holding on, a tree branch, or even a log that you sat on. As long as the force of the spell is enough to lift both the object and the character along with all his gear, it is normally accepted. If you are lifting yourself, I'd say a Strength check is required, but otherwise, the vertical movement and gravity should be enough to keep your character balanced during the movement.
For the third, I'd say you need some kind of surface that allows you to easily balance your character (or make Acrobatic checks once per round), or either crouch or sit on the object. Because the spell doesn't describe how precise the movement is, leaving that entirely up to the GM. Otherwise, the movement is not steady enough to horizontally move the object while still maintaining balance. But following the same logic used for the other movements, it is still valid.
Finally, levitation using Telekinesis is also supported by James Jacobs:
Regardless of how they work mechanically, do you approve of using something like this power to:
a) fling a Dwarf holy warrior at the enemy and
b) bludgeon a hobgoblin officer to death with a stuffed owlbear?
I would approve of it using the spell telekinesis so I suppose I approve of it via the use of similar effects!