Omiyamairi & Okuizome Questions

About the Omiyamairi:

1) Is the bib and hat set ever worn for something else, or is it a one-time thing? I can find a cheap set on amazon.co.jp, or rent from the photo studio if we choose to do formal photos, but I don't mind springing for a nicer/more expensive set if its something that either she'll wear again for another ceremony (like the Okuizome maybe? Seen some pictures that look like it...) or can be passed onto her kids, etc.

2) What does the kiddo wear besides the bib and hat, or does it matter?

3) For the kimono the adult wears around the baby, it seems like it has a special tie that goes around the back, so you can't just use any old furisode. Is this kimono called something particular? Is it the same one the girl wears for her 3 or 7 year old ceremony, or is it a one time thing also?

4) Reading about it, it seems like the mother usually doesn't carry the child for the ceremony. My MIL lives in the US, and my husband doesn't really have much family left we could ask. Would it be weird for either me to just carry her anyway, or to ask an older friend of the family (my husband's childhood best friend's mom)? (Am I thinking too much into this?)

About the Okuizome:

5) I'm not that great of a cook. I'm going to ask a cooking teacher I know if she could do a private lesson to help me prepare the food, but if that doesn't work out, is it something we can get catered? I think I could handle most of the small dishes, but not sure about the tai fish!

6) Is there a particular significance to where the stone comes from? Any smooth stone ok?

7) Is there a special name for the lacquer set used to present the meal, and (again), is it something that is used again in another ceremony? Like I said, I don't mind springing for an expensive one if it's important!

8) Last question, it seems that while in the past the Omiyamairi was supposed to be a few days after 1 month old, these days as long as you do it before the Okuizome, it's fine. But would it be weird to do them at the same time?

Is there anything else I should know about these? I appreciate any help!