[RPG] Does Levitate cancel (horizontal) inertia

Inertia is not part of the movement rules of the game

A drow runs at her maximum speed, and jumps over a cliff, activating her levitate spell-like ability.

If this drow runs at her maximum speed, she can't possibly activate her spell-like ability because that takes a Standard Action. She would need to have the ability either as a free action or as a swift action. Running, in Pathfinder, is a full-round action, and even if she were to simply double-move, that would also consume all of her actions for the turn. At best, she can make a single move action and activate her spell.

From the Magic chapter, on Spell-like Abilities:

A spell-like ability has a casting time of 1 standard action unless noted otherwise in the ability or spell description.

You are right in that she can move horizontally normally, but she would have to activate her Levitate ability before running into a cliff.

Levitate does not have any inertia cancelation effect, or even a gravity cancelation effect, and you cannot use momentum to sling-shot yourself (or another target) forward because that's not part of the spell's effect. The spell allows you to move the target by spending a Move Action, it doesn't even cancel their fall if they jump off a cliff with Levitate already cast on them:

Levitate allows you to move yourself, another creature, or an object up and down as you wish. A creature must be willing to be levitated, and an object must be unattended or possessed by a willing creature. You can mentally direct the recipient to move up or down as much as 20 feet each round; doing so is a move action. You cannot move the recipient horizontally, but the recipient could clamber along the face of a cliff, for example, or push against a ceiling to move laterally (generally at half its base land speed).

A levitating creature that attacks with a melee or ranged weapon finds itself increasingly unstable; the first attack has a -1 penalty on attack rolls, the second -2, and so on, to a maximum penalty of -5. A full round spent stabilizing allows the creature to begin again at -1.

From a rules-as-written perspective, the spell can only do what's in its description and whatever other rules it could interact with. As there are no rules about inertia in the game, the spell couldn't possibly be affected by that rule. Everything else is GM Fiat and likely also a house-rule.

Will the character's inertia make her move horizontally, while she keeps her altitude constant (or rising, or going down) by carefully using levitate?

She will not. The character who cast Levitate must spend a move action to make the movement from the Levitate spell. What she could do is keep using her move actions every turn to cross the obstacle by using the walls or ceiling to crawl/climb without any risk of falling, as described under the spell.

If there's no obstacle, will she even stop?

Obstacles are relevant to her up/down movement, a ceiling would prevent the target from moving up, the floor would prevent her from moving down. Similarly, another creature or object could prevent this movement. Otherwise, her movement stops (midair, mind you) as soon as all of her movement and jumping distance has been covered, falling to her death.

But there are gravity rules in the game

On the other hand, we have rules for Gravity, even though Low Gravity doesn't modify your jumping distance in any way:

In an area with only a third of standard gravity, for example, PCs can jump three times as high and as far and lift three times as much. (Movement speed, however, stays the same, as moving in great bounds can be awkward and difficult to control.)

However, in areas of No Gravity (which is actually very low gravity), your movement speed is actually affected and you could do exactly what you described in your answer and slingshot your character forward:

Movement is difficult, and creatures without something to push off from often find themselves floating helplessly. When a creature does manage to find something to propel itself off of, it can choose to move in any direction, but at half speed. Double-moves and charges are still possible, but running is not. If provided with sufficient handholds, a creature with a climb speed can move along a wall at full speed, as can any PC who succeeds at a DC 20 Climb check (adding her Dexterity bonus).

Note as well that a creature that moves in a given direction continues to move in that direction at the same speed each round (without the cost of a move action) unless it is able to change its motion by latching on to an object or creature, pushing off in a new direction, or creating thrust of some kind (all of which are considered move actions).

There is also a spell called Gravity Sphere (wizard 5), which allows you to create a 30-feet-radius sphere of no gravity. As such, it would allow you to propel yourself forward following the same rules for no gravity, as long as all the movement happens inside the area of the spell.

Can this effect be used by the drow to "jump over" a charm of 30 metres/100 feet?

It cannot. Again, there is no inertial movement unless you are in zero gravity environments, and the spell doesn't allow horizontal movements either.

So, as you can see, there are rules covering the effect you are looking for, and those mechanics, in no way, interact with Levitate, or even the Fly spell.

What about the fly spell?

Fly gives you a fly speed, as such, you couldn't use it to prevent you from falling, or even creating this slingshot effect mentioned previously, but you could use it to fly using part of your movement speed. Since the spell grants you 60 feet fly speed, you could spend a move action to walk towards a cliff, and then simply take another move action to fly over it for another 60 feet. Even though you should just double move or run while flying, to be honest.

But note that Fly, just like Levitate, does not prevent you from falling or taking falling damage. So simply running towards a cliff and spending all your actions will likely drop you into the cliff for the remaining of the round, falling down at least 200 feet (as described under Falling).