Even though many people would say that North America is a Christian society, many children have not heard the good news of God’s saving love. Thus, many children need a precatechumenate before we begin the more formal catechesis of the period of the catechumenate. For more information about this, see this article.

That depends upon your diocese. Some dioceses have set an age for confirmation of Catholic children that is older than some of the peer companions. So in that case, they could not be confirmed until they had reached the age set by the diocese. Even in dioceses in which younger Catholic children may be confirmed, I’m not sure it is such a good idea. The initiation of the unbaptized would ordinarily take place at the Easter Vigil. The focus of the Vigil should be on the unbaptized, and not on Catholics who are being confirmed. It’s a little hard to give a definitive answer without being in your circumstances, but that would be my rule of thumb.

Yes.

In Paul Turner’s, When Other Christians Become Catholic, he cites Canon 885.2, which says:

A presbyter who has this faculty [the faculty to receive non-Catholics into full communion and confirm them] must use it for those in whose favor the faculty was granted.

Turner then goes on to say:

Consequently, if a priest is receiving a baptized child into the Catholic Church through the rite of reception, he must confirm the child as well. This should win ready approval from the parties involved because the child will benefit from the gifts of the Spirit at a very early age.

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There are pros and cons for this. However, I lean toward keeping the children in the main worship space for the liturgy of the word and dismissing the unbaptized children after the homily. I don’t think it’s important that children understand every word of the readings. I do think it’s important that they master the ritual of what we do during the liturgy of the word. And I think it’s important that they be seen as true catechumens along with the adult catechumens. If the children are having difficulty understanding the readings, it might help to ask their parents to go over the readings with the children before Mass, perhaps using a children’s lectionary version. It might also help to ask the children to focus particularly on the gospel and not worry too much about the other readings. Ask them to remember one thing they hear in the gospel each week and be ready to talk about that. The parents can help here, too, reminding the children just as the Alleluia starts to pay attention.