Is a crocheted tallit considered kosher, so long as the material follows the halacha? Does it have to be relatively solid, or would a "granny square" type tallit also be kosher? Does it need to have no holes whatsoever (planned), or can it be designed with gaps?

Yes, it's kosher to crochet a talit with "granny squares", for it's considered a "begged", an article of clothing, and there's no problem with the fact that there are small gaps there.