Don't worry about over-watering the plants. That's one of the beauties of raised beds, they drain so well it's tough to over-water them. This also means raised beds dry out fairly quickly. Just make sure it's damp. If you see water pooling up, it's time to stop watering.
It doesn't matter how many seeds you dropped in the hole. Just pluck the extra plants that sprout.
One thing that got me through the cold New England winters was starting seeds under florescent lights in the basement. I bet your daughter would get a kick out of that. You can start onions as early as February. Tomatoes in March. Also another suggestion (sorry about the amount of suggestions but I'm excited to help anyone starting out on this great hobby), I really enjoyed getting the FedCo seed catalog every winter. I bet you and your daughter would have a fun time going through it, choosing what you want to plant. The FedCo seed catalog is a fun read, it's not just a listing of seeds. "Armchair gardening" is what we call it. Here is a link to the catalog request page. They also have pdfs you can view but getting the catalog in the mail is more fun.
http://www.fedcoseeds.com/requests.htm
For the tomatoes, I think a traditional cage may not work with your setup. I don't think 6 inches of soil will support the cage and the tomato plants once they are large. Since you planted the tomatoes in the back I think stringing them up a might work best for you. I had trouble keeping my cages upright in a foot of soil. But I found bending the bottom of the cages so the legs spread outright helps provide more support. Also, you'll want to cage them sooner than later so you don't cause any root disruption for the tomatoes or surrounding plants. Here is a link I sent to my mother-in-law who is just starting her own garden regarding pruning and stringing up tomatoes.
https://www.youtube.com/watch?v=qJgA4n-sCE8
I never replaced my soil (aside from the tomato buckets which I did every 2 years). I always just amended it with fresh compost which we made. I tested my soil (sent to a university in the mail) after 4 years of gardening in the same box with the same soil (amended yearly with compost) and the test came back with flying colors. I sent the soil out because I wasn't having luck with some plants. Turns out I just wasn't getting enough sun. Doesn't look like you'll have that problem.
One thing I would stress is just don't worry too much about it. When I started I found myself over-flooded with different opinions on what to plant where, how to do it, blah, blah, blah. Just plant the seeds, observe, sit back and enjoy. Nature knows how to take care of itself.
BTW, where are you located?