You should get a -11 bat (which means that the weight is 11 ounces less than the amount of inches on the bat) and a glove that's about 10-11 inches.
a small size
Depends on his size and position.
One that fits his/her hand.
10 inch but it depends on hand size. Maybe smaller
Youth baseball gloves come in different inch sizes. An 8-year-old, for example, can probably use either a 10-inch glove or an 11-inch glove, depending on their size and preference. Due to such variation, it's important to try them on in the store.
It depends on the size of your child. Most 7 yr olds are going to wear an 11"-11 1/2" glove. Make sure that you get a glove that is easy for them to squeeze when it is on their hand.
A small size glove
The size of the glove depends on what position she plays. This buyers guide should help:http://www.hitrunscore.com/softball-glove-buyers-guide.html
Check here: http://www.baseball-equipment-info.com/baseball-glove-size.html
I would at least go with an 11 inch glove and possibly an 11 1/2. The 9 inch gloves are really small and will not be usable in a year or two. I would recommend that you get a glove that is game ready....it is basically broken in for you. I do not typically agree with the charts out there that recommend the small glove for this age.
It depends on the length of the fingers and sometimes the width but i got an 12". The one that i got works really well. Its a mizuno.