I have to make a few comments on your structure.
1 - 2x4's attached at a 90 degree angle actually make a better structural corner post than gluing them up into almost a 4x4.
2 - The key to prevent racking is triangles. More importantly, it is triangles in the fasteners. The bigger the triangle, the stronger the protection against racking. If the 2x4's are attached using a triangle pattern with the fasteners, it will tend to resist racking. But, the stress on the fasteners may be pretty high and over time they could loosen. The good news is that by joining the corner posts at a 90 degree angle, you made some bigger triangles. Based on what you are after, if it doesn't rack now, I would leave it alone. If it starts to rack later, I would go back and add some short 1x4 braces to reinforce the structure. They should be pretty light so, if you wanted to, you could do it now. The key on the 1x4s is to use lots of screws so that there isn't opportunity to loosen up over time.
3 - As far as the roof structure goes, I think you did a good job, you just need to go from the corners instead of the sides. Again, on the bracing, you should be able to use 1x4s instead of 2x4s, but use lots of screws.
That's my 2 cents.