Here's my experience. I got rear ended, killed both sides of the bumper but was able to save my old bumper and reuse it.
Hi there, 2010 Camry SE, 4-cylinder owner here.
1) Based on what I've explained, and the pictures, am I right? Will I need a bumper replacement?
Yes, since your screw hole next to the clip is trashed, you really need a new bumper.
2) From what you can see, will I need any additional work done?
You need new brackets on the car itself, on my '07 there's no screws to it so it wouldn't hold after impact. I junk yarded new ones.
3) How much would you guess this would cost if I take it to a professional?
Easily $1500+ if using OEM parts
4) Should I take it directly to the Toyota dealer, or is a local mechanic a better bet? My dad has a decent relationship with a mechanic in town who he's trusted for years and years.
I'd recommend a mechanic but use OEM parts, tried a generic one for an LE off eBay, didn't like it.
5) How to I identify the exact Toyota bumper cover part # I need? Once I have the right part number, should I be looking for the actual original Toyota part, or are third party replacements just as good? Where should I be looking to find what I need (online, specific stores, etc?)
You can go to your dealer and have them print the diagram, that's what I did. They'll ask for your VIN when you order as they can paint match it too. 3rd parties are a hit/miss, up to you if you want to try it.
6) What does 'part comes unprimed' mean? I've seen that several times when looking at bumper covers online. Does it have something to do with paint color?
Unprimed means it comes as a raw bumper, as if it was fresh out the factory. You will still need to prime before your color goes on as that insures a good painting surface.
7) How do I make sure that I'm getting a replacement that is the same color as my car? I don't see the parts places listing color, so I'm guessing that if I buy online the part comes unpainted (right?) If that's the case, how/where do I get it painted the proper color? Do I need to take it to the Toyota dealership? Seems like that might be expensive.
Typically unpainted, it's hard to match paint without VIN and most of the online retailers just sell they don't paint or install.
8) I'm still concerned about how I'm going to replace the yellow thing that holds the left back screw (again, see pictures here: http://imgur.com/a/gDTit) - it sits behind the metal. Any thoughts or advice? Will it be easy to remove and then re-attach the metal thing blocking that yellow piece? I feel comfortable with the bumper cover removal/reattachment, but that metal piece seems like it's more than a visual component.
A bit of cutting and tapping will get it back, I messed up that hole too but with patience I got it back.
9) Any other info that might be helpful? Are there any particular reasons I should not attempt to do this myself? Seems like it has the potential to save me a significant amount of money, or end up costing me even more and it'll end up not working out the way I thought.
Nothing wrong with doing it yourself if you have the right materials and tools. I think you can do it as you have no form of frame/panel damage. You're just replacing parts...