The first question is "is the handlebar actually bent?". Brake levers/shifters are just clamped onto the bar, and the clamp may have just slipped. It's not clear from the angle of the picture that the bar may be fine but the clamp on the brifter slipped. You can peel back the hood (back to front) and adjust the clamp if this is the case).
If it is the case that the handlebar itself is actually bent (which I think is unlikely; if this was the case, the brifter would likely be toast), I'd just buy a new handlebar. The stress of bending the handlebar back may increase the likelihood of failure. Plus, handlebars are not very expensive or hard to replace.
As for fixing scratches on shifters, you can buy just the name plate if you want, but if the shifters work fine I wouldn't bother. The part numbers are Shimano Y-6KD98030 and Y-6RR98030 for the ST-5600 levers (look for the exploded view of your shifters on Shimano's website). Then you can find the parts by searching the web for a few bucks.
Finally, I'd give the whole bike a once over as if I was considering buying it used if anything else is wrong, for some peace of mind; there are a ton of questions on buying used bikes on this SE which you can look at for what to check.