Is there a reason why you “grab and pull through” the yarn with the hook over the yarn instead of the yarn over the hook? I’ve never done this with other stitches, but when used with a single crochet, it makes a bit firmer, crossed stitch.
So sorry for the late reply! Yes, you're right! Chain 3 is used when you count your chains as the first double crochet. I usually use chain 2 when I don't count the chains as my first double crochet, but sometimes I just like the look better :)