I'll try too answer some of your questions, but I don't have all the answers.
1. What's a BOV?
A blow-off-valve (BOV) sits in the INTAKE, after the compressor
half of the turbo. The purpose is to vent excess pressure, such as when the throttle plate is suddenly closed during an upshift. It is not normally used to control boost pressure. I don't know what precise mechanisms are used.
A wastegate sits in the EXHAUST. It allows exhaust gas to bypass the turbine
half of the turbo. It is used to control boost pressure, by limiting the turbine's supply of exhaust gas.
2. Fuel Management?
Any ECU that can run the engine by itself
is a "stand-alone" ECU, so I suppose the stock ECU qualifies
But the APEX-i S-AFC would not qualify, because cannot be run by itself.
I don't want to comment on the big injectors, becuase I'm liable to be wrong
I know some other engines' kits use a fuel-pressure riser, indexed to boost pressure, to provide additional fuel , but that strikes me as a very sloppy solution. Also I believe the fuel-pressure riser goes on the return line to the fuel tank, but the Celica has a returnless fuel system.
I think the XS turbo originally added a return line and fuel-pressure riser, but now they have appear to have moved on to the Power FC ECU for fuel control.
3. Why is the stock fuel pump not adequate?
I don't know the specifics.
4. Air path?
The intake air always comes through the compressor half of the turbo and then the intercooler, even at idle.
More Info: http://auto.howstuffworks.com/turbo.htm