Btw, based on pics I took in showrooms and shows, all '05-'09 Innova (J, E, G, V variants, D-4D, VVT-i, M/T, A/T) are equipped with maintenance free batteries from the assembly plant in Sta Rosa. Outlast is the brand TMPI uses.
It does have openings but not one you can easily turn as in a knob. But rather the openings on the maintenance free is flat and need to be opened using a coin (see pic).
Re: fog lamp.
If you have a written agreement with the dealer that they will provide a genuine OEM foglamp then they must do so. In the absence of such agreement, I think the dealer wouldn't be liable for installing an "imitation" foglamp in your vehicle.
re: rusty exhaust pipe.
This is a more common problem for VVT-i owners. For D-4D owners, the black soot from the diesel coats the exhaust pipe and acts as a rust inhibitor.
Singer oil, WD40, etc. these types of oils dry up quickly. What you need to apply is a marine grade waterproof type of oil.