Opening a Matador Brenner?

I have an old Matador Brenner with dirty oil and wig, and I would like to open it.
I will be happy if I can just clean it, but it would be great if I can restore it to working condition.

So far, gentle heat and application of penetrating oil hasn't helped: I have not been able to unscrew the burner.
Also, the wig adjustment is stuck, so there is no way I can get the wig out.

Any ideas on how to approach this are welcome!

Do you know if the metal lid is permanently glued to the glass reservoir, or whether I can try to screw it off?

This one has kept me puzzled for a while, I really expected to be able to screw the glass bowl off. Well, this makes life a little easier: only one connection to focus on. Thanks!

I soaked it in warm soapy water for one day. The water forced the lighter oil out, which is a welcome side effect. Also, it loosened parts up, so I could remove the crown and a cilindrical part from the burner (this was possible because the air vents were damaged by a previous owner, so the remainder could be bent out a little). Now I can see that the part that moves the wig is completely turned down, and the round top of it seals the entrance to the glass reservoir. However, there is a big opening, lengthwise along the core of the burner, which is for ventilation?

The whole thing is incredibly dirty, so I guess it is a good idea to let it soak a little more...

Im a little confused by the wick adjustment mechanism for this type of burner: the top disk seems to be glued to the rest of the burner, through waxy soothy dirt. Is there someone out there who could provide a diagram for this part?

I let it boil for an hour in hot soapy water, and it opened effortlessly!