Is my Trek FX2 really toast? I have a 2016 or 2017 Trek FX2 (if critical I'll look up exact year). Ride it daily for shopping, going to the gym and such. Store it outside, unprotected from rain.  Took it to the store I bought it at to have new pedals and break pads installed. Guy at the shop noticed that the headset was loose. After opening it up (lots of rust inside) he's basically saying it's toast and he wouldn't recommend repairing it. Why? Because combined with the other things that need to be done, the total bill will come to about half the price of a new bike. Better to go with a new bike because this old one will just cause exponentially increasing maintenance and replacement costs going forward.   I don't know the first thing about any of this and there is also a language barrier. I speak the local language where I live reasonably well but for technical discussions like this one it leaves a lot to be desired. (Thus it's also possible that I might have misunderstood parts of what he told me.) 

My question here is first whether this sounds plausible, or whether the guy is possibly trying to pull the wool over my eyes. 

And secondly if it does sound plausible, is there a better option than simply going for a new bike? How about replacing the frame and headset with a new one?
The fact that you've left the bike out in the rain the whole time and that the chain is rusty suggest that you've not been looking after it. It doesn't surprise me that it would now be damaged beyond economic repair.

I used to have a Trek 721, which I think is a predecessor model to the FX2.  Mine was kept under a roof and lasted longer than yours but, after several years of use, it too hit the point where enough stuff needed replacing that it wasn't worth doing so.  From the way it's been treated, it sounds plausible that your bike would now be at that point, too.

I suggest that you take it to another bike shop for a second opinion and then decide how to proceed.  Assuming that they say essentially the same thing, you have two options: either pay half the cost of a new bike and have a bike that will work for maybe another six to 18 months, or pay the whole cost of a new bike and get a new bike.