I'm still pretty new to all of this and have only started serious tinkering 6 month ago
Disclaimer 2: I etch my boards myself, therfefore i tend to not use anything less than 10 mil
Couple of thoughts on the pcb:
I can't see myself etching anything like this at home, so if at some time you might persuade your mom to let you do it, you will need to adjust quite a bit.
If you stick with one trace width, make it thicker. You have a 500mA fuse and the trace leading to and from it are 6 mil. This will work, but the traces might already start to heat up by 5-8 degree Celsius (10-15 F), before the fuse blows.
I usually pick something pretty thick as a standard (32 mil for self etched, maybe 16 mil for professionaly made) and only decrease trace width when necessary.
You can change the width of multiple traces by selecting them (one by one, or with the "selection rectangle") and using the wrench tool.
Also 6 mil trace might cost extra.
Do you know where you want to manufacture your board? If so look up there rules regarding thickness, spacing, etc. Maybe they even have DRC (Desing Rule Check) settings, which you can use to check your board before sending it to them.
The idea of the capacitators C1 and C5 is to smooh any irregularities in the power supply for the ICs, therefore they should be as close as possible (in terms of electric connection) to the respective power pins. As it is, they are all pretty much near the power regulator.
You have some very tight areas, and some very roomy ones, use your space! For example below the ATMega you have four traces running in 0.7mm distances. You even have dents in one to make room for a via. But to the right of it you have 50 mm of completly free space. This will also help with manufacturing tolerances and might make soldering easier.
Be carefull what you finally use as the silkscreen. If you print over any pads you might not be able to solder to them later on.
In general you should avoid sharp edges in traces. This isn't really a problem for anything on the scale of an arduino, but it might be a good thing to start doing this early on.
Just to make clear:
This is not bad for your first board, there are a few neat areas in there. I just agree with jabber that it might be to ambitious.
If i design a shield, i usually got through 3-4 prototypes, before i'm happy. And even after that i still find ways to improve it. I have the advantage, that i can make one prototype Friday evening, test it on Saturday, make some changes and etch a new one on Sunday. If you make new revisions, you will have to pay and wait for it each time.
I would recommend always testing a circuit on a breadboard first (depending on the complexity this can take days), and for smaller things even using stripeboard or perfboard for the first few prototypes.
Sorry for the long post, i hope i didn't sound to negative.