We find losses in the first few days are reduced by keeping the chicks and hen in a small 2x2 metre enclosure, it lets them get used to scratching but stops them getting into harms way. We have a pervasive, sticky plant here that will trap chicks up to about three weeks old (they're just not strong enough to pull themselves off of it, mom wanders off, easy pickings for crows, squirrels, ants etc.), once over a week old they can last long enough for us to find them usually. Also hawks seem much keener to take very small chicks rather than week old ones. Also other chickens aren't that friendly to little chicks and a peck on the head can kill a day old no trouble.
As they're your first I'd keep them in for at least five days, give them some dirt to dig in and if you have termites they just love them. Make sure your water bowls aren't too deep, if they are put stones or a brick in it so that if they fall in they can get back out.
Our cats were never a problem with chicks, but if yours are only used to big chickens a small chick might seem a little more interesting, even as a toy. It's great when the cats and chickens get along - keeps hawks, snakes, lizards and other cats away.
but the hen continued to sit on 6 eggs for several days after that
Some of our hens are up and out the same day, others will sit on eggs for a whole week after all the chicks that are going to hatch have hatched but they do give up, eventually. They still care for the little ones, just keep them near the nest while they wait. Only about four weeks ago we had had one girl (aptly named 'Madly') sit on her eggs for five weeks and eventually we took her off - all nine eggs were completely clear - she had no idea but in general they know what's going on.