What are those top tube (often chrome) handle-looking things I see on a lot of fixed gears (like in the attached photo)? And what's their point?

I tried searching elsewhere to figure this out, but don't even know what to search really. And I don't know any hipsters.

They're top tube protectors. Sometimes they're just some handlebar tape, sometimes they're a big pad that covers the whole top tube. In your photo it's just to protect from the handlebars swinging and hitting the top tube (not an issue on a bike with brake cables). The bigger ones are to protect from bike racks and U-locks.

Brilliant.

Thanks.

many builders will gladly put them on the bike at your request.

The wheels are mismatched. Am I out of touch with current styles? (probably)

Who died?

with FG styles, Yes, very.

How about aerospoke rear, spoked front?

Are you trying to be uncool? Everyone knows it's aerospoke front, spoked rear.

aerospokes have a tendency for the track hubs to break loose of the wheel in the rear if you skip/skid/apply lots of back pressure, thus spoked backs, aerospoke fronts.

perfectly logical reason for what would seem to the uninformed out-of-touch person to be questionable aesthetics

I just call them top tube chrome things.

pictured on that bike looks like a kashimax fivegold top tube protector, basically a rubbery clear material over a metal clasp that protects your top tube from dents if you crash or moronically knock your bike over and your bars whip around and hit it.

also it looks like that frame has long-shen lr-15 track ends in the back which i always thought were cute