The vast majority of air compressors sold in the UK are mains powered - in fact when I was looking a year or so ago I couldn't find any affordable petrol powered ones (my garage doesn't have mains electricity) - I ended up buying battery tools instead.
Continental say 5/32" or 4mm- https://www.continental-tires.com/car/tire-knowledge/tire-care-maintenance/tread-depth
Some winter and all-season tyres come with an extra set of wear bars set at 5/32" or 4mm for when they're considered unsafe for snow use but they're probably still good for snow/ice-free roads right down to the normal wear bars. On snow/ice-...
If the tires look OK, they are probably fine.
Issues to check for:
cracks in tread and sidewall
bubbles in tread and sidewall
cuts, embedded foreign objects
Storage conditions make a big difference. Storing tires in dark plastic bags away from sun light and ozone sources makes them last longer. Tires not mounted on a vehicle last longer.
Some research over at https://www.hubcaphaven.com/p/8892/aly59444-bmw-x5-wheel-silver-painted-36116761929.html show that these wheels (based on the partnumber 6761929) have an offset of 40mm. Given that '40' appears in the information given, I'd be pretty solid with that number.
Short version: try it and see.
The 15" tires are 2.6% larger in overall diameter than the 16" tires. This will make your speedometer read 2.6% too high and effectively reduce acceleration of the vehicle by 2.6%. At 2.6% this is not really an issue for most people, e.g. when the speedometer indicates 70 mph you are really going 72 mph - not a ...