I think parenting by rewards is inherently problematic, for reasons such as what you're experiencing. Rewards generally teaches kids to desire the reward, and not whatever it was you were using the reward for.
1) So it seems your child doesn't respond well to rewards? That means you have to find other incentives. A more direct approach would be to make the thing itself appear more appealing. I personally would rather see my children do the thing for the thing itself and not for an arbitrary reward. Try to appeal to the inherent value of the thing you want to make happen. If you can't find one, question why the thing should be done. If the value is only for you, and not the child, you can usually say something like "I'd really appreciate if..." Pleasing you and is an important value to your child. Make sure you also express your gratification afterwards.
2) This is not something I'd stress personally. If the child is busy exploring one aspect of the world, you may consider how important it is that your still young child can focus on all areas at once. But given that this is your aim, if your child is not inclined towards competition, make sure you steer away from competitive elements in introducing novel tasks, lest the task should seem unappealing in several regards at once. Keep it playful. Model play: stack blocks on your own with no pressure or expectation of the child to follow suit. Just let the child notice that this is also a possible avenue of play. Follow the natural inclination of your child. Draw letters on your blocks and stack them to build simple towers of two to three letter words. Latch on to the child's inclination to imaginative play and make the blocks into characters and tell a story, using them as action figures, and make the story unfold such that the figures are piling up on top of each other.
3) I want to throw in a caveat that if it turns out your child simply isn't very competitive, that there are virtues in that too. Ultimately, our jobs as parents are to help out children grow to achieve their goals; not to set them. But again, if this is your aim: when young children enjoy competition, what they enjoy is usually winning. Don't introduce competition into an area the child already has an aversion to, for the same reasons as in 2). Make sport out of things the child already enjoys, and let them win. But be mindful that the introduction of competition isn't runining the fun in the things your child does enjoy. If you see a tendency towards that, I'd back off. Optimising for competitiveness has the risk of suggesting to the child that their self worth is linked to their performance, which I think can be to their detriment.