Amer-icans often do activities which do not include their children. A gift is not expected unless the occasion is a birthday or a similar kind of event. Yes, you should politely offer to help. Often your host will enjoy talking with you while you work together in the kitchen. This is an easy and informal way for you and your friend to get to know each other better.
Expectations differ significantly between families.
Waiting for your host to tell you where to sit is considered polite. If your host has children, they may be very excited about having you sit next to them. Also, many families may pray before eating. Americans may take larger portions of food than you are used to in your country. Feel free to ask for more if you would like.