As you get older (late teens) your parents will start getting more confidence in you riding around the streets. 13 nearly 14 is very young so it will take a lot of persuading for them to change their opinions at the moment.
Mesomorphs are a type of body structure thats naturally athletic, have broad shoulders and supposed to be the 'perfect' build. Anyway I don't think your too light. Being a light cyclist has huge advantages, just look at the pro cyclists.
For me I felt a quite a loss of bike control while riding with Bullhorn bars, but I can see the benefits on short races. Best to go for the aerobar attatchment on your standard drop bar so you can alternate between them.
The surgery will heal it quicker but will obviously leave marks and cuts that you won't ever get rid of. Depends on the pain and situation your in I guess.
Shouldn't regret post race, only look forward to what can and will be. Its hard not to though I know, hate starting a sprint too late and knowing I would have won if I went a few seconds earlier!
If your looking for an entry level road bike you could check out some bike stores to find a model and try and find that model cheaper online somewhere such as eBay.
Don't spend too much on your first bike as you don't know how much your going to cycle on it yet and its easy to sell a cheaper...