It sounds are indirect over the engine. That ticking sound does not occur on my mini cooper at all. Now what you can live with; it's probably in good shape.
Hose did not change anything I heard no pop off valve during deceleration.
I would check for play in the turbo. The pin wheel while the car is turned OFF. A tinny bit of play is usual and nothing to fret over. If it is moving in and out up and down. Your turbo is worn out.
I say that because it sounds kind of like someone has a hand brake on the crankshaft where it slows down and not really flutters down. What the RPM like?
The electronic blow off valve I would check second they become old and worn out. I would replace this spring and put the electronic housing that this spring goes in back on the turbo charger.
Great alternative to complete replacement BOVs
Then I would pull off the upper heat shield and get a better look at the vacuum turbo actuator arm or Rod and see if it is bent. The vacuum actuator housing does not look like anything does not look like anything special. But that one has a real rhino naugahyde (L.O.L. not real naugahyde!) of a diaphram in there. And under heat and stress and pressures of opening the wastegate door can actually bend.
So I would check to see if the rod is bent.
After that I would address that timing chain or at least inspect it at this point by removing the valve cover and checking the upper guide rails as well as the lowers with a flashlight to see if they are broken or in distressed.
If everything where o k I would put the valve cover back on using:
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As far as the starter My recommendation is to replace it with a Bosch
Bosch (OE Reman) SR0466X Starter - Mini | 0001106018090 0986018837 12411489995 12411517328
You get a good return on the core for a little over 100 dollars U.S. provided your present one is a SR0466X like the mini coopers came with stock.
Whipping and winding sound does not sound right and I have not heard yet about an issue where they would need to have shims put in them to align.
The helpful thing is that if it is the rod you can bend it back out with a heavy bushing pick or even a crowbar very very slowely. Needing to be un bent due to the actuator arm sticking.
And that would clear up my hypothesis of the engine sounding like it has a handbrake on the crankshaft. When the wastegate door fails to open after building boost it will continue to shove air into the engine.
Making it rev down slower. When the foot is off the pedal.