Coolant work, if it's never been done, I'd highly recommend overhauling the ENTIRE cooling system. I broke it down to the cost of oem parts and it would be less than $800 if DIY.
Water Pump LR097165
Water Pump gasket LR049370
(2x) - $32ea ($64)
Oil cooler pipe LR028136
Oil cooler pipe o-ring LR030593
Front crossover pipe LR018275
Rear crossover pipe LR109402
Front coolant temp sensor LR041442
(eurospare vs hard to find oem) - $23
BMW brass bleed screw
(Concentrated, I believe) - $38
Total cost = $770 before tax and shipping
Peace of mind for the next 100,000k = PRICELESS!
I'm sure you can find better deals if you really searched around. I highly recommend sticking with oem on cooling parts, The only non-oem parts would be the water pump gasket, coolant temp sensor (hard to source), bleed screw, and coolant. I completely flushed out the coolant till clear to swap in dexcool. dexcool is abundant everywhere and most of my trips are very remote and could pick up cheap dexcool anywhere.
Vibration, there's a whole thread on this https://www.landroverworld.org/threads/2013-lr4-weird-humming-noise.30757/post-239237
. I recently did this myself and it helped a lot.
Damper bolt IYP500080
Edit: Almost forgot, swap out swollen nuts to solid 1 pieces. Something like this, https://a.co/d/69jJLmF