In my experience, the registry of the aircraft plays an important part in the prevalence of metric hardware on Airbus aircraft, but I have not found any Airbus products that are completely standard or completely metric--you'll need both, depending on the work you are performing.
Metric
Yes, the simple answer is yes - Japanese cars in general need metric tools - make sure you have plenty of 10mm wrenches for sure.
There are over 1,000 tools and sets of tools you will need. Start by buying a basic Automotive tool set. Add sockets up to 2 1/2 inches and the equivilant in Metric. Over 1 1/4 you can get by with only SAE or Metric. Wrenches to match. Add to the kit from there
This depends, although most likely standard unless you have a Eunos model which is the European Miata, which those use metric.
Yes, all the hardware and fittings are sized in metric, but there are American equivalents for some. (8mm = 5/16, etc.) There is no American equivalent for 10mm.
Common mechanics hand tools. Sockets, ratchets, open & boxed end wrenches. More than likely metric.
I'm not familiary with the odyssey, but you'll need a metric wrench (I don't know what size, though, but it'll be metric.. 13mm or 15mm are the likely sizes), and a slotted screwdriver (to separate the ring terminals from the posts).
A sewing machine and leather-working tools.
You'll need some metric sockets. 3/8" drive will be fine. Maybe a small extension and the ratchet. Not to many tools involved.
not sure what size nut it is on hub,but it will be a metric size. also depending on what side of vehicle you are working, it may be left hand thread
Generally you will need basic metric wrenches, and metric sockets and possibly a torx head socket on some models. Also jackstands and hydraulic jack.
What work needs done? You will need a good set of metric tools, and the rest depends on what is wrong with the engine.