I got into an accident where my handlebars got bent. They are very firm and do not seem to budge with force, but I'm a small guy. Can they be fixed? Can I do it myself? What tools would I need? How much would it cost for someone else to do it? Is this considered major damage, or something minor?
Additionally, how difficult would it be to fix these scratches/marks?
Damaged Handlebar
Undamaged Handlebar
Marks/Scratches
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.
Consider the scratches as war wounds. They're only cosmetic, but they show you ride; that you're not a cycling poseur.
If the scratches really bother you, consider bogging it with automotive filler, then file and sand to shape, and paint. It will add grammes of weight though!
As for adjusting the hoods, you need a 5mm (maybe 4mm, maybe 6mm) hex driver tool, aka an allen key. You probably has one on your bike multi-tool, but sometimes a longer shop one gives more torque.
Unpeel the top of your brake hoods like this:
Then push the driver down the inside between the rubber and the brake to the pinch bolt.
Loosen, adjust, retighten, and finally reclip the rubber to the brake.
From the first picture, it looks like the shifter has been knocked out of position but there's no damage to the bars themselves. If that's the case, it should be an easy fix. A good bike shop wouldn't charge much to put it right. The scratches on the shifter are only cosmetic, and I'd be surprised if it was cost-effective to replace the parts unless you (or the aforementioned bike shop) happen to have the bits to spare (maybe from a previous repair or upgrade). I've got a few scratches on my (very similar) shifters, and while they bothered me at first, I don't notice them now.
