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.