We love your kids---we really do. However, only kids invited are those who are apart of the wedding party. Therefore, If your invitation says "one-child" then yes, if otherwise then we loved just you and your plus one.
No, check out the Travel page for all the info you need.
If your invitation says "and Guest," then yes, if not, we would prefer it if it was just you.
Cocktail, please. But we want you to feel comfortable, so if those shoes are too high or that tie is too tight, then don't be ashamed to take off those shoes, loosen that tie and have a blast!