Grappling (PHB, p. 195) states:

When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.

Movement and Position (PHB, p. 190) states:

Your movement can include jumping, climbing, and swimming. These different modes of movement can be combined with walking, or they can constitute your entire move.

(1) Therefore, if the steeder has a creature grappled, it won't be able to jump, unless the grappled creature is small or smaller. Alternatively, some effect might have increased the steeder's speed to 60+ without a grapple, and the halved speed is therefore still 30+.
Note that dashing doesn't help you here - it only increases your movement (PHB, p. 192), while your speed is still unchanged (e.g. at 15 feet).

(2) The steeder's leap is different from the regular jumping rules in the PHB, hence, all relevant rules can be found in the steeder's description. Since it can either expend all its movement to jump 90 feet or not at all, there is no halving of the jump distance.
Either it can jump 90 feet, or not at all (barring the regular jump rules, which of course still apply).

(3) Grappling also states:

The condition specifies the things that end it, and you can release the target whenever you like (no action required).

Breaking up your move (PHB, p. 190) only mentions

You can break up your movement on your turn, using some of your speed before and after your action. For example, if you have a speed of 30 feet, you can move 10 feet, take your action, and then move 20 feet.

Now, releasing a creature doesn't require an action, but I think the intent is clear - yes, you'd be able to release it during the jump. That also makes sense from a logical point of view, which is what I always try to take into consideration when I make any rulings as the DM.

No. Movement forced by a spell is not willing movement.

"Willing movement" (and being "willing" in general) is never defined in the rules, though it's referenced in spells like booming blade (SCAG, p. 142). Thus, since it's not a defined game term, we default to the natural English definition of the term.

According to Dictionary.com, "willing" means "disposed or consenting; inclined". However, the movement from the infestation spell (XGtE, p. 158) is forced by the spell on a failed Con save; the target has no choice about whether to do it, so it's certainly not doing so of its own volition. As such, it seems clear that movement forced by such a spell is not willing.

Jeremy Crawford supports this interpretation in an unofficial April 2016 tweet in which he addresses a similar question about the dissonant whispers spell and its interaction with booming blade:

Would you take damage from the second part of Booming Blade if you fail a save against Dissonant Whispers and move away?

Booming blade hurts you if you move away willingly. Dissonant whispers forces you to move—doesn't trigger BL.

but if they move after whispers in their turn (to get back into melee, for example) that counts, right?

Yes.

Crawford provides the same explanation in an earlier unofficial tweet in February 2016:

Would the movement caused by a failed save on Dissonant Whispers be willing or unwilling movement?

If a spell forces you to move, as dissonant whispers does, you're not moving of your own volition.

Does that mean the movement from Dissonant Whispers doesn't provoke opportunity attacks?

The movement in dissonant whispers can provoke opportunity attacks, since it uses your reaction (PH, 195).

The same logic would follow here regarding infestation and booming blade; the spell is forcing the targeted creature to move, so the creature is not doing so willingly. Thus, booming blade's extra damage would not trigger.

(Sidenote: infestation does not trigger opportunity attacks either, because it moves the creature without using its action, reaction, or movement.)