Legacy neutral (not ground)
Yes, this is kind of a big mess, because it's a 3-wire connection (hot-hot-neutral) with neutral masquerading as ground. It is not ground. It is neutral.
Normally that's illegal, even in 1980, but you see how the neutral wire is a disorganized bunch of strands field-twisted together? That actually makes it leeeegal. That's SE cable, and the neutral becomes a web that surrounds the other two conductors. It's a service cable, so it's neutral not ground. You were never allowed to use /2 w/ground cable, because you could have as easily used /3 w/ground. I suspect that rule was to allow the supply chain to use up their stock of 40A SE which has little other use, since 40A services are outlawed.
So, the hood tapping the bare aluminum for neutral, is actually fair game. It is neutral. The problem is that the range hood is also bootlegging ground off this neutral. That is not allowed, unless you are a range. Or to be more precise, the range is allowed to make a 3-wire hot-hot-neutral connection, and then internally attach the range chassis to neutral with a jumper.
This 3-wire range connection still isn't a good idea. If that neutral wire breaks, it will electrify the chassis of the range. As wired, it will also electrify the chassis of the range hood.
Honestly, if this were me, I would do one of two things for sure: Either a) put a GFCI on this supply circuit, or b) retrofit ground. Or both.
I would fastidiously insulate the webbed neutral wire coming off that SE cable, so it is entirely insulated from the faux grounding of the steel junction box. I'd use tape and heat shrink tubing, and for style points I'd go with white or gray shrink tubing; the inspector will like that a lot.
Then, I would run a #10 bare ground wire from the ground lug on this junction box, back to any of a) the panel, b) any grounded 30A+ circuits going back to the panel; c) any non-flexible conduit going back to the panel; or d) any part of the panel's Grounding Electrode System, i.e. the copper wires heading off to water pipes or ground rods. Not water pipes directly.
Then, I would make a 4-wire connection to that range, removing the range's N-G jumper, and grounding everything to those steel junction boxes. This ground retrofit will provide the best safety; I'd rank it slightly above a GFCI for safety.
The conversion of the SE cable's neutral wire to an, um, neutral... is perfectly legit, because it's SE cable and that is neutral. The fastidious insulation of it is vital to ground doing its job.
If you do not retrofit ground, then it becomes vital to fit a 2-pole GFCI breaker. This will be an expensive piece, but it protects you from a common and lethal failure mode of 3-wire-connected ranges and dryers.
Splicing aluminum is a big deal, though.
As NoSparksPlease points out, those splices won't cut the mustard. The aluminum wire is too big for Alumiconns.
So you will need to get appropriate Polaris style connectors to make the splices between the AL conductors (H-H-N) and the range and hood. That is a deep 4" square box, but it's still going to get very full very fast.
One trick is to get an accessory ground bar intended for a service panel, and hack it up to give the number of voids you need (1 per wire). But then it must be fastidiously insulated with electrical tape; that's hard to get right, and inspectors dislike it because they can't inspect a wad of electrical tape.
That range hood
First, wiring that range hood into the range circuit is definitely illegal unless you retrofit a ground, because the range hood needs a real ground. However, I don't believe it can share the range circuit unless you get a variance from your local inspector. (who supposedly inspected and signed off on this, yes?)
Nor can it share a kitchen countertop receptacle circuit, unless again you get a variance.