Is there a time of day that hawks don't hunt?
While hawks are often more active at certain times of day, a hawk can hunt from sunrise to sundown and may take prey at any time.
So, sadly-- no, there is no absolutely 'safe' time of day.
Since I live in an area with lots of houses and small yards that are fenced in would the hawks even bother to hunt here?
As their habitat shrinks and more hawks are adapting to suburban and urban environments, yes-- hawks kills in small yards are becoming more frequent. If there is a hawk in your area it might actually be more of a danger to your flock because urban hawks are less likely to be fearful around humans. Young, first year hawks are often the biggest problem because they are not real smart about what they can and cannot handle in terms of kills, yet. It really depends on your area! You may never see a hawk or you might see them frequently. A merlin regularly takes pigeons right against the side of my parents house, and they have a very small fenced lot (with two large dogs, even!).
If you are concerned, since you have a small yard you have a few options. Some people have had great success with stringing surveyor's ribbon (often hot pink or orange, and thin like plastic) every few feet, horizontally, from the top of fencing. If this is too gaudy for you, you can also try a heavyweight fishing line.
We have a lot of red shouldered hawks where I live too, and even though I am very rural they seem less fearful than the other hawk species and are always buzzing my (covered) chicken run when I am out there.
Screech owls should not be able to take a full grown chicken. Maybe chicks.
Whatever you decide, best of luck!