2003 Audi TT - Convertible - 1.8 - automatic - 166k

This car was purchased as a No Start project..
And someone else has been trying to fix the car before I got it...
Lower dash removed, fuse box hanging down, ie wire tracing..

Status: Powers up.. will not crank.
Turn Key on, dash lights up, fuel pump runs.
Turn Key to Start. .Nothing..

Testing completed:
1. Add a remote starter switch to the starter input plug.. The car starts and runs fine.. I drove it 20 miles...

I have the starting wiring diagram.. What I find in the car is not the same.?

Current state:
1. I removed the steering column covers to access the back of the ignition. see diagram below.
I found that the small red/black wire is the starter output pulse.. ie key to start.. signal out..

2. The red/blk wire goes to the back of the relay box at the drivers knee. it enters the rear of the box.. and exit at the red circle.

3. When the relay is triggered it sends a pulse to the Blue Out put/blue wire to the fuse box to 4 fuses..
Fuses 28- fuel pump, 32,34,43 - Engine-timing - petrol -

Question 1. Why do these fuse need a starter pulse?

Question 2. What are the 3 Engine- Timing- Fuses For?

Question 3. I have a relay 167 in that position.. Remember Someone else has been working on this car before I got it..
I trace the starter input signal into the relay box.. The out put lug is circled in red. The 167 Relay does NOT have a spade connector in the output position.
DO I HAVE THE WRONG RELAY???

Question 4. If I were to trace back from the starter, the black wire the triggers the starter to engage.. Where does it terminate inside the car?? It disappears into the harness at the firewall and I can not find it in the cabin any where.. Where does it connect to get triggered??

I humbly await your wise words!!
Kenneth
Crankless in TN

 

Finally got a picture of the relay center in my '02 fwd 180hp TT.
Hope it helps.