the + still needs some sort of appearance of providing turns as a dwarf ordered to push across one will still make a turn on it. the new + looks like the N-S E-W are forced and turning isn't allowed.
I think, in real life, it does not seem that two railways that intersect at 90 degrees have normal fork with the possibility of changing the direction of motion - there is always a rather confusing denouement - but I'm not a specialist railroader, I can be wrong.
How in DF works + fork have no idea - never used rails.
Аnyway, I drew what you described. Previous post updated.
number 3 is more like how it functions, it can allow a dwarf to "guide" it but the implied direction of movement in "pushed" or "ride" mode is straight unless a wall is present.
how carts work:
lets say you have this setup:
1---+---3
|
2
where 1,2,3 are defined track route stops.
If a dwarf is ordered to push|ride at point 1 he will give the cart a shove and the cart wont turn at the + and continue until it reaches 3(and if there is no wall beyond 3 and no actual track stop building that can break it, it wont stop it will just keep going). At that point a dwarf will retrieve the cart and drag it to point 2 along the straightest route...even over no track. if 2 is also a push|ride he would then shove it and it would continue north past the + if there is no wall, otherwise stopping at the + if there is a wall past it. At which point the dwarf drags it to point 3 and if it was the same thing... at least then the cart would reach point 1 and hopefully there is a wall and it stops there and a dwarf doesn't have to drag it back to one.
If the dwarf is ordered to guide it, he would move it from 1 to 2 then 2 to 3 then 3 to 1(if 2 and 3 are guides too). at the + or T or any other turn he would make the appropriate turn needed to finish the path. guided routes across connected track is the easiest to ensure completion. Of course this means a dwarf has to follow the cart everywhere.
Fun is when you design complex automated cart systems with ejectors, impulse ramps, decelerator rooms, dumping track stops, and all the other fun stuff that one can build. at which point the + T intersections are the least useful unless they are built on ramps. Even more fun is when you design it with riders and make it into a roller coaster and try not loose your passenger as you move it through system... The greatest fun is when you use it to eject material in complex assault systems that allow you to grapeshot the tavern with a cart full of daggers...
The main point of carts and tracks is to remember that shoved carts will follow curves only when they are 1-in-1-out or if its on a ramp and only 1 out is to the lower floor. The cart will remain on the track as long as its under derailment speed(which without impulses or other ramp tracks is easy) or there is a wall blocking the forward movement(and thus also blocking derailment), forcing the cart to stay on the track and seek a single lower exit from the tile. additionally track tiles main purpose is to reduce the friction of the cart against the surface.
so if a cart is moving at decent speed and reaches a set of tracks that look like this:
----|||||||+++----
It will move across these as if they as a straight line. even if a dwarf is told to guide across these... the dwarf will get confused and just start dragging the cart across the straight distance... which means he will drag across these and the friction is less anyway on these tiles... well as long as there isn't a straighter path available that circumvents these tiles,such as this:
+------------------1
|WWWWWWWWWWWWWWWWW WWWW - walls with a gap in it. and the track doesn't connect so the dwarf will just drag from 1 to 2 through the gap.
+----|||||||+++----2
I could build some actual track images and explain some of this a lot better with images. but I think that covers what we was discussing.