Yes the round "discs" that the cam bears down onto are the shims, these come in lots of sizes so you can adjust the clearance, it's ok to do swaps with each other, as they wear evenly(should) as the cam is slightly off centre so they rotate a little each press to keep wear even.
How many presses does the plunger take to get hard ?, white smoke indicates air in the fuel system, this is the most likely entry point for air.
I would check all the pipes on the turbo/inlet for splits, but they shouldn't be unduly noisy, the tappets are easy to do, just a bit long winded.
Get a note pad and pen measure gaps, take tappet out one at a time measure tappet, put back, do all this on all eight, so you've established the gaps you have the shim thickness and the gap needed, you will find some of your existing shims can be moved to give correct gap on different cylinders, then buy the new gaps you need from ford or similar, about £3 each, they will often do trade in's as well.
Shim is same on a huge amount of engines from peugeot, seat, fiat, vw, citroen, renault etc etc if you get stuck.
tabetha