In reply to goldmember:
They're decent efforts for your first attempts at races - lots of people would be very happy with a 45 minute 10k and a 1.49 half.
Weight will have a bit of a bearing, and losing 8-9 kg will make life a bit easier and running a bit quicker. Don't be put off by the fact that bigger folk were finishing in front of you - the more you race, the more you'll realise that there are all sorts of shapes and sizes, and a bit of extra weight isn't necessarily an indicator of ability.
To improve, I'd suggest two things. One is to join a running club, if there is one local to you. Running with other people is almost always good for you - you can learn from more experienced runners, and you'll find yourself running faster if you train with other people. Training on your own an be quite lonely and you can end up sticking to a single speed.
The other thing is simply to run more. If you're doing 3 sessions a week, try to increase it to 4 or 5 times a week. It already sounds like you're mixing things up, which is very good. Adding in more miles will generally improve strength and endurance.
As for rest after races - it's all about how you feel. Some people will run the day after a race, just to ease the legs out, some will take a day or two to recover. Depending on how hard you race, you might take the training a bit easier for a few days.
You certainly sound to be in fine shape for another half before the end of July - good luck with it.