Cemetery and TV Hill St are the same thing; both reference former occupants (at different times) of the site at the top: The large fenced plot along Lanark St (primarily to the east, but also the parking lot on the west side) was the home of WPXI TV until about 2007; in the late 1800s up to I think maybe the 1950s it was a cemetery.
Lanark St changes name because it didn't always go all the way through--at some point it ended at the lower end of the cemetery, though the trolley line kept going. It was eventually extended to the top of the hill, and sometime later made continuous with the street it lined up with--but since that street already had a name, it kept it. On the other hand, the three sections of Hazelton look like someone laid a ruler across the map and drew a road, then discovered when they went to build it that there were some insurmountable grades involved and so made it discontinuous. (That bend at Suffolk St? Originally two different streets. Most of this stuff has method, but there be madness in it, too.) I suspect some of these plans were done by people who'd never seen the place, as there are 'roads' drawn on the map which would rival Canton Ave in grade. (Who knows, maybe there were originally staircases involved.) Old property maps show an awful lot of empty squares all owned by the same people, suggesting they were divided up for sale as buildable lots but were never built on.
Carrie does, in fact, continue east of Henderson--next time you're up there, look for a large red structure standing above the fence. This is the top of the Carrie St Steps, which go down one level (about five or ten stories) to Sprain St. Similarly, Biggs Ave doesn't change names into Glenrose; Glenrose terminates at Biggs Ave, which happens to only be drivable in one direction from that intersection--it's a staircase to the north.
Bark, Wurzell, etc you will note changes names at curves. If you look at a very old map (such as
http://arcg.is/2u2h3FY), you will note there were originally many more streets there; between the lack of proposed development, the hollowing out of Pittsburgh's population after the 1950s--remember, there were once nearly three times as many people in the city as there are now--and the construction of the Parkway North in the valley just east of there, many of the extensions were never built or were taken out, with the result making it look like one continuous street--but each section kept its names. (As an aside, having lived a few years nearby and spent some time in that area, I suspect the folks who live back there don't mind that people who don't live there find it confusing, and would rather everyone else just stay out.)
The curve of Glenrose into Hazelton is similar to Bark/Wurzell/Brule/Magnet; Hazelton was originally supposed to continue south to Rising Main, part of which survives as the northern end of Warren St.