But,
 

How will I know that mine is?

I just told you it was.
I can tell from your pictures that it has all the correct parts.

Not convinced. Do a VIN search.

Or, easy as looking at that glovebox sticker. It will have FE5 which is the code for the SS suspension package.
FE5 was only available on the SS.

And LNF which designates the 2.0 turbocharged.

Relax, take a breath, we'll help you through this.
All the cosmetic mods you mentioned, do as you see fit.

I'm more performance minded, so for that I recommend the TTR front engine mount first. It will greatly reduce wheel hop and torque steer, making the car safer to drive aggressively.

If the engine and turbo check out to be healthy, a tune would be another great performance mod. If you go for a tune, you probably should upgrade the charge piping and intercooler. If stock tune is good enough, skip the tune.

The TTR rear sway bar would be great, after one or both of the above.

I think TTR also makes inserts for the transaxle mounts, that would go well with the engine mount.

I thought you meant the picture of yours was real.
 

I CAN'T SEE the glovebox sticker.
It's way in the back, behind where the box itself sits.

I'm having a problem picking the right motor mount to order. TTR offers many, some are on sale right now. It would be nice if mine was on sale. :)

Contact Aaron at turbo Tech racing. Hell hook you up with everything specific to your car. If you do a search on here for Turbo Tech racing, his posts will show up and you can send him a PM. Or you can e mail turbo Tech racing directly. It should go to him. That's how I got into contact with him about my rear anti sway bar.

Cool! I will certainly contact him
 

I haven't been too interested in getting to know my vehicles in over 40 years. Not since I lost my 69 GTO in a bad decision.
I really want to do everything right with my SS and understand how to do things to it to make it mine.

As stated before. RELAX. Take a breath.

Now. The RPO sticker in the glovebox should be on the door itself. Then just look for the codes that designate that it's a real SS.
FE5= SS suspension
LNF= 2.0l turbo charged engine
1SS= Package

Attachment 22008

Attachment 22009

Here is the TTR page for HHR.

HHR - Turbo Tech Racing

Click on the drivetrain button for the engine mount. You can find the sway bar by clicking on the suspension button.

You can PM Aaron here
https://www.chevyhhr.net/forums/priv...o=newpm&u=4515

I think these are the trans mount inserts, but they are not on the HHR page, but on their cobalt drivetrain page, so ask Aaron.
Turbo Tech Racing Transmission Race Mounts Chevrolet Cobalt 05-07 / Saturn Redline 05-07 2.0L - Drivetrain

EDIT: Those trans mounts also say for manual trans. This might be a mistake, so definitely ask Aaron, if you are interested in them. Or he can give you a link to the correct ones.