Even Minifilia is surprised that crystals and willpower is all that seems to be required to create a primal comparing it to Good King Moogle Mog. She even says as such. She didn't postulate that Shiva may not have been a summon. They never doubted that for a second and these are the people in the realm that are experts on the topic. So as far as we know based on the way the characters treat the events of 2.4 we can deduce that she is indeed a primal since they seem very content with that result. As such she has all the abilities of a primal such as tempering even though we just didn't see her use it. Honestly, we never gave her a chance to use it since we took her down the moment she was summoned(born?).
*This part is speculation*
As for her merging with Shiva that does seem to be possible since this was a unique summoning in the story. It's also possible that she was acting in a similar way to the artifact the Ascians keep giving to the beast tribes. They use these artifacts it to summon their primals in addition to massive amounts of crystals. Judging by her using Haedalyn's quote it's entirely possible Iceheart has echo and was able to summon shiva due to having echo thus acting like a medium in place of the artifact. This follows along with the existing story where Minifilia is trying to figure out what the echo is exactly and the quote is one of those "so the plot thickens" kind of moments. I'm very interested in seeing where this plot thread goes.